ChE Exam

Chemical Engineering Thermodynamics

Question 1 (10 points)

A vertical cylinder with a freely floating piston contains 0.1 kg air at 1.2 bar and a small electric resistor. The resistor is wired to an external 12 Volt battery. When a current of 1.5 Amps is passed through the resistor for 90 sec, the piston sweeps a volume of 0.01 m3. Assume
(i) piston and the cylinder are insulated and
(ii) air behaves as an ideal gas with Cv = 700 J/(kg·K).
Find the rise in the temperature of air.

Answer: 6 °C

Question 2 (30 points)

100 m3 of carbon dioxide initially at 423 K and 50 bar (50 × 105 Pa) is to be isothermally compressed in a frictionless piston and cylinder device to a final pressure of 300 bar (300 × 105 Pa). Assuming ideal gas behavior (R = 8.314 × 10-2 bar·m3/kmol·K),
(a) Calculate the volume of the compressed carbon dioxide gas at 300 bar.
(b) Calculate the work done to compress the carbon dioxide gas.
(c) Calculate the heat flow on compression.

Answer: (a) 16.7 m3; (b) 896 MJ; (c) -896 MJ

Question 3 (20 points)

In the vicinity of the triple point, the vapor pressures of liquid and solid ammonia are respectively given by
ln p = 15.16 − 3063/T and ln p = 18.70 − 3754/T
where p is in atmospheres and T is in Kelvin. What is the temperature at the triple point? Also calculate the triple point pressure.

Answer: T = 195.2 K; p = 0.588 atm

Question 4 (20 points)

106 Joules of heat are transferred from a reservoir at 327 °C to an engine that operates on the Carnot cycle. The engine rejects heat to a reservoir at 27 °C. Determine the thermal efficiency of the cycle and the work done by the engine.

Answer: 50% thermal efficiency; W = 0.5 × 106 Joules

Question 5 (10 points)

A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains 1 kmol nitrogen at a certain temperature and pressure, the other contains 1 kmol of CO2 at the same temperature and pressure. The membrane is ruptured and the two gases are allowed to mix. Assume that the gases behave as ideal gases. Calculate the increase in entropy of the contents of the cylinder. Universal gas constant R = 8314 J/kmol·K.

Answer: ΔS = 11526 J/K

Question 6 (10 points)

Air expands steadily through a turbine from 6 bar, 800 K to 1 bar, 520 K. During the expansion, heat transfer from air to the surroundings at 300 K is 10 kJ/kg air. Neglect the changes in kinetic and potential energies and evaluate the irreversibility per kg air. Assume air to behave as an ideal gas with Cp = 1.0 kJ/(kg·K) and R = 0.3 kJ/(kg·K).

Answer: Irreversibility per kg of air = 0.074 kJ/K