Problems
Mixture Properties
An ideal gas mixture consists of 6 kg of O2, 5 kg of N2 and 12 kg of CO2.
1. Determine the mass and mole fraction of each component.
2. Determine the average molar mass and the gas constant of the mixture.
3. Compute the partial pressures of all components when the total pressure is 2 bar.
4. Compute the entropy of mixing between mixed and unmixed state.
Heating of Mixture
A piston-cylinder device contains a mixture of 1 kg of H2 and 2 kg of N2, initially at 200 kPa and 280 K. The mixture is heated at constant pressure until the volume is three times the initial volume. Determine the temperature of the final state, the total heat transferred, and the change of entropy of the mixture. Use tabulated property data.
Isobaric Cooling of Mixture
A piston-cylinder device contains a mixture of 0.75 kg of N2 and 2 kg of CO at 300 kPa and 860 K. Heat is now transferred from the mixture at constant pressure until the volume is one third of the initial volume. Determine the heat transfer, the work done, and the change of entropy. Use tabulated property data.
Mixing of H2 and CO2
An adiabatic rigid tank is divided into two parts. One part contains 4.4 kg of CO2 at 25 ◦C and 200 kPa, and the other part contains 1 kg of H2 at 80 ◦C and 400 kPa. After the divider is removed, the gases mix and the mixture assume a final equilibrium state.
1. Determine the equilibrium temperature and the equilibrium pressure.
2. Compute the entropy generated in the process.
Assume constant specific heats at 300 K for both gases.
Compressor
1. Determine the power to run the compressor.
2. Assume that the compression is polytropic, and determine the polytropic exponent. Then find the exit pressure.
Adiabatic Turbine
The combustion product in a gas turbine system consists of nitrogen, oxy- gen, carbon dioxide and water with the following mole flow rates: n˙ N2 = At turbine inlet, the pressure is 12 bar, and the temperature is 1500 K.
Determine the power production of the turbine in isentropic expansion to an external pressure of 1 bar.
Hint: To estimate exit temperature for trial and error, you might want to look at expansion of air first.
Mixing and Separation
1 kg of argon at 10 bar, 400 K and 0.5 kg of xenon at 10 bar, 1000 K are isobarically and adiabatically mixed in a closed piston-cylinder system.
1. Determine the equilibrium temperature of the mixture.
2. Determine the initial system volume, and the volume change between initial and final state. Explain the result.
3. Find the reversible work required for separation of the mixture.
Remark: Both gases are monatomic, with MAr = 39.95 kg
Mixing of Argon and Helium
An adiabatic cylinder is closed by a moveable piston. The cylinder contains 4litres of argon at 150 kPa and a rubber balloon which contains 1litre of he- lium at 3 bar. Both gases are initially at a temperature of 25 ◦C, and the piston rests due to its own weight. Assume that the pressure volume characteristic of the balloon is of the form Δp = a (VB − V0) where Δp is the pressure difference between inside and outside, VB is the actual volume, the reference volume V0 is 0.25litres, and a is a material constant. This implies that the balloon shell stores some energy when stretched. As soon as the balloon has reached the volume V0, there are no further stresses in the balloon, and the balloon shell will just collapse. For simplicity, ignore the thermal mass of the balloon.
A small hole opens in the balloon through which all helium escapes; in the final equilibrium state the gases are mixed.
1. Determine the pressure, temperature and cylinder volume in the final equilibrium state.
Compute the entropy changes for both gases, and the total entropy generated in the process. Compare to the entropy of mixing, Smix, and discuss the difference.