Example Problem with Complete Solution

3B-2 : Internal Energy of Superheated Water Vapor 2 pts
Superheated ammonia vapor is stored in two rigid tanks, as shown below. Can you determine, by observation and reasoning alone, which has the higher molar internal energy, A or B?
     
     
Calculate the difference in molar internal energy between the two tanks using data from the NIST WebBook.
 
Read : Because the water vapor is superheated, it has 2 degrees of freedom. In this case both the T and P must be specified to completely determine the state. Because the state is completely determined, we can use the given T and P values to look up properties like U and H in the Superheated Tables in the Steam Tables.
Diagram: Given in the problem statement.
Given: PA = 1.55 atm PB = 1.55 atm
TA = 23 oC TB = 4 oC
Find: DU = UA - UB = ??? kJ/mol
Assumptions: None.
Equations / Data / Solve:
The internal energy of a substance is the sum of the kinetic energies stored in the vibrational, rotational, and translational motion of the molecules. Tank A has more energy by virtue of its higher temperature. Therefore, it must have the higher intern
We must look up the isobaric properties of superheated water in the NIST WebBook. Use the ASHRAE convention. A portion of the thermodynamic table used in this problem is given below.
T
(C)
P
(atm)
U
(kJ/mol)
Phase
2 1.55 #VALUE! vapor
3 1.55 #VALUE! vapor
4 1.55 #VALUE! vapor
5 1.55 #VALUE! vapor
21 1.55 #VALUE! vapor
22 1.55 #VALUE! vapor
23 1.55 #VALUE! vapor
24 1.55 #VALUE! vapor
The internal energies at the two given temperatures are:
T = 23oC T = 4oC
UA #VALUE! KJ/mol UB #VALUE! KJ/mol
As we predicted, the internal energy of the water vapor in Tank A is greater than in Tank B.
The U of Tank A is greater by:
DU = UA - UB = #VALUE! KJ/mol
Verify: No assumptions to verify this time.
Answers : DU #VALUE! KJ/mol