Problem Set #2
Work, Heat, Energy
1. One mole of methane is heated from 300 K to 400 K. Calculate DU, q, and w at (a) constant pressure and (b) constant volume. Cv,m = 30.86 J/K and is independent of temperature. Assume ideal gas behavior.
2. Calculate the work done when an ideal gas is expanded isothermally from 10 atm, 2.0 L, 293 K to 1 atm if the expansion occurs (a) against Pexternal = 1 atm, and (b) reversibly. Note: 1 atm = 1.01 x 105 Pa; 1 m3 = 103 L.
3. Derive the following equation for the work on reversible expansion of a van der Waals gas .
4. The Redlich-Kwong (RK) equation of state is . Show that the work on an RK gas for a reversible, isothermal expansion is
5. A mole of liquid water is vaporized at 100°C and 1.013 bar. The heat of vaporization is 40.69 kJ/ mol. What are the values of wrev, q, DU, and DH?
6. One mole of perfect gas at 25°C and 100 bar is allowed to expand reversibly and isothermally to 5 bar. Calculate w, q, DU, and DH, all in Joules. Note: 1 bar = 105 Pa.
7. Initially, 5 mol of nitrogen are at a temperature of 25°C and 10 atm. The gas is ideal; Cv,m = 20.8 J K-1 mol-1 and is independent of temperature. Suppose that the pressure is dropped to 1 atm, reversibly and adiabatically. Calculate the final temperature, DU, and DH.
Expansion, Compression (Adiabatic, Isothermal, Reversible, Irreversible)
8. One mole of a non-linear, polyatomic ideal gas is expanded from 500 K, 5 atm to a final pressure of 1 atm. Calculate the work for an expansion that is (a) isothermal, reversible; (b) adiabatic, reversible. [Hint: For a non-linear polyatomic ideal gas, Cv,m =3R; ignore vibrational contributions to the heat capacity.]
9. During the operation of an internal combustion engine, the fuel-air mixture is compressed until the volume is reduced by a factor of 9 (the compression ratio). Assuming g = 1.4 (the value for nitrogen and oxygen), estimate the final temperature if it starts at 25°C and the compression is reversible and adiabatic.
10. A tank contains 20 L of compressed monatomic ideal gas at 10 bar and 25°C. Calculate the maximum work (in Joules) that can be obtained when the gas expands to 1 bar pressure (a) isothermally, and (b) adiabatically. [Hint: Consider Cv,m, Cp,m, and g for an adiabatic expansion of a monatomic ideal gas.]11. An ideal gas expanded reversibly and adiabatically to twice its volume. Its initial temperature was 25°C, Cv,m = . Calculate DUm and DHm.
12. In each of the following cases, an ideal gas expands against a constant external pressure. For each case, decide if the expansion is allowed by the first law, and if so, if the expansion can be carried out reversibly. No explanation is needed.
(a) isothermal and adiabatic
(b) isothermal but not adiabatic
(c) neither isothermal nor adiabatic