# Worksheet: Thermodynamic Changes in Ideal Gases

In this worksheet, we will practice calculating the net heating of and net work done by ideal gases that change pressure, volume, and temperature.

**Q1: **

A gas with a mass of 0.125 kg
is contained in a rigid container
with a volume of 2.5 m^{3}. The gas is heated, increasing its
temperature by 35 K and also increasing its pressure, as shown in the diagram.
Calculate the change in the internal energy of the gas due to its heating.
Use a value of 1.75 kJ/kg⋅K
for the specific heat capacity of a constant volume of the gas.
Assume the heating of the container is negligible. Answer to three significant figures.

- A 87,500 J
- B 11,300 J
- C 5,000 J
- D 24,600 J
- E 7,660 J

**Q2: **

A gas consisting of
2.5 moles
of particles is compressed isothermally,
as shown in the diagram. The gas has a temperature of
360 K.
Find the work done on the gas to compress it.
Use
8.31 m^{2}⋅kg/s^{2}⋅K⋅mol
for the value of the molar gas constant.
Give your answer to three significant figures.

**Q3: **

The diagram shows the changes of volume with temperature of three gases.

Which gas is changing isobarically?

- AGas I
- BGas III
- CGas II

For which gas is work being done to compress the gas?

- AGas I
- BGas III
- CGas II

**Q4: **

A gas of mass 0.55 kg is heated in a flexible container, increasing the temperature of the gas by 10 K and increasing the volume of the gas, but maintaining the gas at a constant pressure, as shown in the diagram.

Calculate the change in the internal energy of the gas due to its expansion. Assume that the work done on the container is negligible.

Calculate the specific heat of the gas at constant pressure. Assume that heating of the container is negligible. Answer to three significant figures.

**Q5: **

A gas with a mass of 1,000 g is heated at constant pressure and is being expanded. The gas is placed into a container equal in volume to the volume of the gas after its expansion. The pressure of the gas is decreased by cooling the gas at constant volume. The changes in the pressure and volume of the gas are shown in the diagram. The temperature of the gas decreases by 4.5 K when it cools and the specific heat capacity at constant volume of the gas is 1.25 kJ/kg⋅K. Find the net change in the internal energy of the gas.

**Q6: **

The changes in the pressure of a gas with volume are shown in the graph. The lines represent an isothermal change and an adiabatic change from the same initial temperature. Which line represents the adiabatic change?

- ABlue
- BOrange

**Q7: **

A gas with a mass of 0.25 kg is compressed, changing its pressure and volume as shown in the diagram. The initial temperature of the gas is 303 K.

How much work is required to compress the gas?

What is the final temperature of the gas? Answer to three significant figures.

If the internal energy of the gas is the same before and after its compression, find the average specific heat capacity of the gas during its compression. Answer to three significant figures.

**Q8: **

The diagram shows the change in the pressure of a gas as its volume increases for three different thermodynamic processes.

Which process shows the pressure and volume of the gas changing isothermally?

- AProcess III
- BProcess II
- CProcess I

Which process shows the temperature of the gas undergoing a net increase?

- AProcess II
- BProcess III
- CProcess I

Which process shows the temperature of the gas undergoing a net decrease?

- AProcess I
- BProcess II
- CProcess III

**Q9: **

A gas is compressed, changing its pressure and volume as shown in the diagram. The initial temperature of the gas is 324 K.

What is the product of the gas pressure and the gas volume before the compression?

What is the product of the gas pressure and the gas volume after the compression?

What is the change in the temperature of the gas due to the compression?

Suppose the gas is compressed and simultaneously either heated or cooled. The pressure and volume of the gas change such that when their values are plotted on a pressure-versus-volume graph, they form a straight line. What would the temperature of the gas be if its volume was 3.1 m^{3}? Answer to three significant figures.

**Q10: **

The lid of an uninsulated cylinder containing gas is moved downward by a force of 250 N through a distance of 45 cm, as shown in the diagram. The force includes the lid’s weight. The internal energy of the gas after the compression is the same as before the compression. How much does the cylinder heat its surroundings? Give your answer to three significant figures.