Problems on Reversible Processes in Closed Systems

Problems

Water in Tank

A closed rigid tank contains 3 kg of saturated water vapor, initially at 140 ◦C. Heat transfer occurs, and the pressure drops to 200 kPa. Kinetic and potential energy eﬀects are negligible. Determine heat and work exchanged during the process.

Isochoric Heating of Air

2 kg of air are heated in a reversible process at constant volume. The initial temperature and pressure are T1 = 20 ◦C and p1 = 2 bar, and the ﬁnal temperature is T2 = 500 K. Compute heat and work exchanged, and the change in entropy. Draw the process in p-v- and T-s-diagrams.

Water in Tank

A closed rigid tank contains 2 kg of saturated water (liquid and vapor), initially at 0.2 MPa with a quality of 4.65%. How much heat must be added so that the ﬁnal state is saturated vapor? What is the ﬁnal temperature, and how much work is required?

Heating and Melting of Ice

2 kg of ice are initially at −20 ◦C and 1 bar. The ice is isobarically heated, then melted and further heated until a temperature of 20 ◦C is reached. Determine the heat required for this process, the volume change, and the work. Determine also the heat required to heat the ice to 0 ◦C and for melting at 0 ◦C. The heat of melting at 1 bar is hsf = 333.1 kJ , and the speciﬁc heat of ice is cice = 2.1 kJ .

Freezing of Water

1.6 kg of liquid water are initially at 15 ◦C and 1 bar. The water is isobarically cooled, then frozen and further cooled until a temperature of −15 ◦C is reached. Determine the heat required for this process, the volume change, and the work. The heat of melting at 1 bar is hsf = 333.1 kJ , and the speciﬁc heat of ice is cice = 2.1 kJ .

Condensation of Steam

Steam (water vapor) initially at 30 bar, 450 ◦C is isobarically cooled until the volume is one half of the initial volume.

1. Draw the process in a p-v- and in a T-s-diagram with respect to saturation lines.

2. Determine heat and work for the process when the initial volume was 2 m3.

3. Now the volume is ﬁxed and heat is supplied. At what temperature is the saturated vapor state reached?

Lowering of a Piston

A freely moving piston with cross section A = 0.1 m2 and mass m = 2 t closes a cylinder ﬁlled with air; the external pressure is 1 atm. The initial state in the cylinder is V1 = 0.3 m3, T1 = 500 K. Heat is withdrawn, and the piston moves down as the volume of the gas decreases. The piston movement stops when the volume reaches 2/3 of the original volume, but there is further cooling until the temperature is 270 K. Compute the mass of air in the cylinder, and the total amounts of work and heat exchanged. Draw the process in p-v and T-s-diagrams.

Cooling of Air

10 grams of air at 1400 K, 150 bar are cooled in a closed system. The total heat withdrawn is 7936 J and the ﬁnal temperature is 600 K. The cooling occurs ﬁrst at constant pressure (from state 1 to state 2), and then at constant volume (from state 2 to the ﬁnal state 3). Compute ﬁrst the temperature at state 2, and then the pressure at state 3. Also determine the work done by the process.

Isentropic Compression of Saturated Liquid-Vapor Mixture Saturated liquid-vapor mixture of water at 25 ◦C with a quality of x = 0.9 is compressed in an adiabatic reversible process to 175 bar. Determine the temperature of the ﬁnal state, and work and heat per unit mass.

Isentropic Expansion of Air

Air is isentropically expanded in a closed system from T1 = 25 ◦C and p1 = 1 MPa to p2 = 2.5 bar. Determine heat and work exchanged per unit mass. Draw the process in p-v and T-s-diagrams.

Isentropic Expansion

Neon and air are expanded isentropically from 1000 kPa and 500 ◦C to 100 kPa in a piston-cylinder device. Which gas has the lower temperature after expansion? Why? Compute the work per unit mass for both.

Isentropic Compression

Which of the two gases—neon or air—has the higher ﬁnal temperature as it is compressed isentropically from 100 kPa and 450 K to 1000 kPa in a piston- cylinder device? Compute the work per unit mass for both cases.

Isentropic Expansion of Superheated R134a Vapor

Cooling ﬂuid R134a in a closed system is initially at 1.2 MPa, 50 ◦C. Then the cooling ﬂuid is expanded in an adiabatic reversible process to 0.12 MPa. Determine the temperature of the ﬁnal state, and work and heat per unit mass.

Isentropic Expansion of R134a Vapor

Cooling ﬂuid R134a in a closed system is initially at 1.6 MPa, 60 ◦C. Then the cooling ﬂuid is expanded in an adiabatic reversible process to 0.32 MPa. Determine the temperature of the ﬁnal state, and work and heat per unit mass.

Expansion of Air

Air (ideal gas with variable speciﬁc heats) at 1400 K, 50 bar is expanded in a piston-cylinder system until its volume is 12 times the initial volume. Determine work and heat per unit mass (a) when the expansion is isentropic, (b) when the expansion is isothermal.

Isothermal Compression of Water Vapor

In a piston-cylinder system, a mass of 20 kg of water vapor initially at 3 bar, 1200 ◦C is isothermally compressed to 50 bar.

1. Determine heat and work for this process based on the property tables of water.

2. Assume water vapor at these conditions can be described as an ideal gas and compute work and heat based on this assumption. Compare with the result of the exact calculation and discuss the diﬀerences.

Evaporation and Expansion

As part of the processes in a low temperature Carnot engine, R134a undergoes the following process in a piston-cylinder system:

1-2: Isothermal evaporation and heating from saturated liquid state at T1 = 60 ◦C until the volume is 13 times the initial volume.

2-3: Isentropic expansion to p3 = 0.28 MPa.

1. Draw the process in a p-v- and in a T-s-diagram with respect to saturation lines.

2. Determine heat and work for the process when the initial volume was V1 = 20 litres.

3. What would be the thermal eﬃciency of the corresponding Carnot engine?

Polytropic Compression of Oxygen

Pure oxygen is compressed in a polytropic process with polytropic exponent n = 1.25 so that the ﬁnal volume is half the original volume. The initial temperature is 300 K, the ﬁnal pressure is 10 bar, and the work done is 40 kJ. Determine the ﬁnal temperature, the initial pressure, the mass of oxygen, the heat exchanged in the process, and the change in entropy. Draw the process in p-v and T-s-diagrams.

Polytropic Compression

Argon gas, initially at 1 bar, 100 K, undergoes a polytropic process with n = 1.5 to a ﬁnal pressure of 17 bar. Determine the speciﬁc work and heat transfer for the process. Argon can be treated as an ideal gas; recall that it is a monatomic gas, so the speciﬁc heats are constant.

Polytropic Expansion

Helium gas, initially at 20 bar, 200 K, undergoes a polytropic process with n = 1.2 to a ﬁnal pressure of 2 bar. Determine the speciﬁc work and heat transfer for the process. Helium can be treated as an ideal gas, recall that it is a monatomic gas, so the speciﬁc heats are constant.

Polytropic Compression

Radon gas (Rn, MRn = 222 g ) initially at 4 bar, 400 K, is compressed in a piston cylinder system. After compression the measured pressure and temperature are 12 bar and 600 K, respectively. Assume that the process can be described as being polytropic, and determine the polytropic exponent n.

Then determine the speciﬁc work and heat transfer for the process. Radon can be treated as an ideal gas; it is monatomic, hence the speciﬁc heats are constant.

Compression of Air

Air at T1 = 227 ◦C, p1 = 1 atm is compressed in a piston-cylinder device to 1/3 of its original volume. Compute the work and the heat transfer per kg of air when the compression process is (a) isothermal, (b) isentropic, (c) isentropic with constant speciﬁc heats (cold air approximation), (d) polytropic with n = 1.4, (e) polytropic with n = 1.1. Draw the process curves in p-v and T-s-diagrams.

Irreversible Expansion of Helium

An adiabatic and rigid container is divided by a membrane so that one third of the container holds 1 kg of helium at 300 K and 100 Pa while the other part is evacuated. The membrane is destroyed, and the gas undergoes a rather fast and irreversible process until it assumes its stable equilibrium state.

1. Compute temperature and pressure in the equilibrium state, and the change of entropy for the process.

2. Design a reversible compression process that will bring the gas back to its original state (i.e. ﬁlling 1/3 of the container, 300 K, 100 Pa) and compute the work and heat exchange required.

Ice and Saturated Liquid-Vapor Mixture

An insulated piston–cylinder device initially contains 0.01 m3 of saturated liquid–vapor mixture with a quality of 0.2 at 120 ◦C. How much ice at 0 ◦C must be added isobarically to the cylinder so that after equilibrium is reached the cylinder contains saturated liquid at 120 ◦C? Hint: The process is isobaric, work is done.

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