Example Problem with Complete Solution

7A-1 : Process Paths and Cyclic Integrals 4 pts
Consider the cycle made of path A followed by path B shown below.
     
     
The following integrals have been evaluated.
       
     
       
     
Is this cycle reversible, irreversible or impossible?
 
Read : This is a straightforward application of the Clausius Inequality to a thermodynamic cycle interacting with two thermal reservoirs.
Diagram: See the problem statement.
Given:
-24.7 kJ/K
41.3 kJ/K
Find: Is this cycle reversible, irreversible or impossible?
Assumptions: None.
Equations / Data / Solve:
The Clausius Inequality is:
Eqn 1
If the cyclic integral is ... positive, the cycle is impossible
... negative, the cycle is irreversible
... zero, the cycle is reversible
Since the cycle is made up of two steps, A & B, we can expand Eqn 1 as follows:
Eqn 2
Now, we can plug in values from the problem statement.
16.6 kJ/K
Because the cyclic integral is greater than zero, the cycle is impossible.
Verify: None.
Answers : Because the cyclic integral is greater than zero, the cycle is impossible.