# Worksheet: Thermodynamic Processes

In this worksheet, we will practice calculating the work done on or by gases that undergo a combination of thermodynamic processes and calculating the change in their internal energy.

**Q1: **

One mole of an ideal gas is initially in a chamber of volume m^{3} at a temperature of
.

How much heat is absorbed by the gas when it slowly expands isothermally to twice its initial volume?

Suppose the gas is slowly expanded to twice its initial volume by first decreasing the pressure at constant volume and then expanding the gas isobarically. How much heat is transferred in this case?

Calculate the heat transferred when the gas is expanded quasi-statically to twice its initial volume by expanding the gas isobarically, then decreasing its pressure at constant volume.

**Q2: **

An ideal gas expands isothermally along the path , as shown in the accompanying diagram. The gas does J of work along this path.

How much heat does the gas exchange along ?

The gas then expands adiabatically along and does 400 J of work. When the gas returns to along , it exhausts 100 J of heat to its surroundings. How much work is done on the gas along this path?

**Q4: **

A gas undergoes the process shown in the accompanying diagram. When the gas expands along , it does 500 J of work and absorbs 250 J of heat. When the gas expands along , it does 700 J of work and absorbs 300 J of heat.

How much heat does the gas exchange along ?

When the gas makes the transition from to along , 800 J of work is done on it between and . How much heat does the gas exchange along ?

**Q5: **

Consider the closed path shown in the diagram.

What is the change in internal energy for the process represented by the path?

How much heat is exchanged in the process represented by the path?

If the direction in which the path is traversed is reversed, how much heat is exchanged in the process represented by the path?

**Q7: **

Several quasi-static processes are shown in the accompanying diagram. In each case, pressure is in atmospheres and volume is in liters. The values of pressure and volume corresponding to the points plotted on the graphs are: Point 1 ( atm, L), Point 2 ( atm, L), Point 3 ( atm, L), Point 4 ( atm, L), Point 5 ( atm, L), Point 6 ( atm, L), and Point 7 ( atm, L).

Find the work done during the process in case (a).

Find the work done during the process in case (b).

Find the work done during the process in case (c).

Find the work done during the process in case (d).

Find the work done during the process in case (e).

Find the work done during the process in case (f).

**Q8: **

Consider a transformation from point to point in a two-step process. First, the pressure is lowered from 3.00 MPa at point to a pressure of 1.00 MPa, while keeping the volume at 2.00 L by cooling the system. The state reached is labeled . The system is then heated at a constant pressure to reach a volume of 6.00 L in the state .

Find the amount of work done on the path.

Find the amount of heat exchanged by the system when it goes from to on the path.

**Q9: **

The state of 45 moles of steam in a cylinder is changed in a cyclic manner from , where the pressure and volume of the states are (35 atm, 18 L), (56 atm, 18 L), and (56 atm, 36 L). Assume each change takes place along the straight line connecting the initial and final states in the P-V plane.

Find the net work done by the steam in one cycle.

Find the net cooling of the steam over the course of one cycle.

**Q12: **

An ideal gas is at an initial pressure, volume, and temperature of
Pa,
m^{3}, and
320 K respectively. The gas
then expands to a volume m^{3}. Use a value of
for the ratio of the molar heat capacities of the gas.

What is the final temperature of the gas if it expands isothermally?

What is the final pressure of the gas if it expands isothermally?

- A Pa
- B Pa
- C Pa
- D Pa
- E Pa

What is the final temperature of the gas if it expands quasi-statically?

What is the final pressure of the gas if it expands adiabatically and quasi-statically?

- A Pa
- B Pa
- C Pa
- D Pa
- E Pa

**Q13: **

Three moles of a monatomic ideal gas are at a pressure of 6.8 MPa and occupy a volume of 4.0 L. The gas is expanded isothermally until the volume is doubled. The gas is then cooled isochorically until the gas pressure is 2.6 MPa, reducing the gasβs temperature. The gas is then compressed isothermally until its volume is again 4.0 L, but this time at a pressure of 3.5 MPa. Finally, the gas is heated isochorically to return to the initial state where its volume was 4.0 L and its pressure was 6.8 MPa.

What is the net work done by the gas?

What is the net heating of the gas?

**Q15: **

A tank contains 105.0 g chlorine gas (), which is at a temperature of and an absolute pressure of Pa. The temperature of the air outside the tank is . In determining the properties of the gas, use a value of 70.9 g/mol for the molar mass of .

What is the volume of the tank?

What is the internal energy of the gas?

- A J
- B J
- C J
- D J
- E J

**Q23: **

What restrictions exist on the transfer of mass and energy into and out of a closed system?

- AIn a closed system, both mass and energy cannot be transferred in or out of the system boundaries.
- BIn a closed system, no mass may be transferred in or out of the system boundaries.
- CIn a closed system, no energy may be transferred in or out of the system boundaries.
- DIn a closed system, no work may be transferred in or out of the system boundaries.

**Q24: **

What set of thermodynamic processes are used to form a Carnot cycle?

- ATwo isobaric processes and two adiabatic processes.
- BTwo reversible isothermal processes and two adiabatic processes.
- CTwo reversible isentropic processes and two adiabatic processes.
- DTwo irreversible isothermal processes and two adiabatic processes.