Example Problem with Complete Solution

3B-2 : Internal Energy of Superheated Water Vapor
2 pts
Which has a higher molar internal energy:  the superheated water vapor stored in Tank A or the superheated water vapor stored in Tank B?  What is the difference in molar internal energy between the two tanks?  Use data from the NIST WebBook.
Figure 1.
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.
Given: PA =
1.5
 atm PB =
0
 atm
TA =
200
 °C TB =
150
 °C
Find: ΔU = UA - UB =   ??? kJ/mol
Assumptions: None.
Solution: 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
Verify: 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.
       
Temperature (°C)
Pressure (atm)
Internal Energy (kJ/mol)
Phase
140
1.5
46.2
vapor
150
1.5
46.479
vapor
160
1.5
46.756
vapor
170
1.5
47.032
vapor
180
1.5
47.306
vapor
190
1.5
47.581
vapor
200
1.5
47.855
vapor
210
1.5
48.129
vapor
The internal energies at the two given temperatures are:
T = 200°C T = 150°C
UA =
47.855
 KJ/mol UB =
46.479
 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:
ΔU = UA - UB =
1.376
 KJ/mol