An ideal
gas is contained in a pistonandcylinder device in which the system moves from state 1 to state 2.



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































a.) If T_{2} is greater than T_{1}, show that the ΔS_{12} is greater if the process is isobaric than if it is isochoric. Sketch
the isobaric and isochoric process
paths on PV and TS diagrams.



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































b.) Use your TS Diagram from part (a) to show that an isochoric path passing through a
state has a greater slope than an isobaric path passing through the same state.



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































c.) If P_{2} is greater than P_{1}, show that the ratio of ΔS_{12} for an isothermal process to ΔS_{12} for an isochoric process
is (1  g). Sketch the isothermal and isochoric proces paths on PV
and TS diagrams. 

















































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Read : 
Sketch the process in parts (a), (b) and (c) first
to get a better understanding of the processes. 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































For part (a) use equations relating entropy to C_{p} and C_{V}. 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































For part (b) recall that the slope on a TS Diagram is (dT/dS). 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































For part (c) determine DS for each process and determine the ratio. 





































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Given: 
A closed
system consisting of an ideal
gas with constant specific heat ratio g. 
^{} 















































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Find: 
Part (a) 
For the process where
the T increases from T_{1} to T_{2}: show that DS is greater if the change in state
occurs at constant P than if it occurs at constant V. 




































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Sketch PV and TS Diagrams
for the process. 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Part (b) 
Show on a TS Diagram that a line of constant specific
volume passing through a state has a greater slope than a line of constant P. 



































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































Part (c) 
For the process where
the P increases from P_{1} to P_{2}: show that the ratio of DS for an isothermal process to DS for a constant specific volume process is (1  g). 





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































