Ideal Gas Law Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Ideal Gas Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The ideal gas law relates the pressure, volume, temperature, and amount of an ideal gas in one equation.

If you squeeze a gas, heat it, or add more particles, the other gas properties must adjust in a predictable way.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Ideal Gas Law starts by identifying what is warmer, what is cooler, and what energy or state variable changes.

Common stuck point: Students often know a formula related to ideal gas law but skip the recognition step: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships?

Worked Examples

Example 1

medium

A gas at

P_1=200000 \text{ Pa}

V_1=0.1 \text{ m}^3

T_1=400 \text{ K}

is moved to

V_2=0.05 \text{ m}^3

T_2=300 \text{ K}

. Find

P_2

Answer

P_2 = 300000 \text{ Pa}

First step

Combined gas law:

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

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Example 2

medium

A gas does work expanding from

0.02 \text{ m}^3

0.05 \text{ m}^3

at constant pressure

150000 \text{ Pa}

. Find

W

Example 3

medium

Why does substituting

25^\circ\text{C}

instead of

298 \text{ K}

into

PV=nRT

give a wrong pressure by what factor (roughly), if everything else is correct?

Example 4

hard

A scuba tank of

0.012 \text{ m}^3

contains

50 \text{ mol}

of air at

290 \text{ K}

. Find the pressure inside. (

R=8.31

)

Example 5

hard

0.01 \text{ m}^3

rigid container holds gas at

400 \text{ K}

and

300000 \text{ Pa}

. One-third of the moles leaks out at constant

T

. Find the new pressure.

Example 6

hard

2 \text{ mol}

of an ideal gas expand isothermally at

300 \text{ K}

from

0.01 \text{ m}^3

0.02 \text{ m}^3

. Find

W

done by the gas. (

R=8.31

)

Example 7

hard

A diver exhales a

5 \times 10^{-6} \text{ m}^3

bubble at

10 \text{ m}

depth where

P_1 = 200000 \text{ Pa}

and

T_1 = 288 \text{ K}

. At the surface,

P_2 = 100000 \text{ Pa}

and

T_2 = 293 \text{ K}

. Find

V_2

Example 8

challenge

0.020 \text{ m}^3

container holds

1 \text{ mol}

of nitrogen and

2 \text{ mol}

of oxygen at

300 \text{ K}

. Find the total pressure (Dalton's law / ideal gas). (

R=8.31

)

Example 9

challenge

An insulated piston cylinder holds

0.5 \text{ mol}

of gas at

0.005 \text{ m}^3

400 \text{ K}

. The piston is pushed in to

0.002 \text{ m}^3

while the gas warms to

600 \text{ K}

. Find the new pressure. (

R=8.31

)

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A gas has

n=2 \text{ mol}

T=300 \text{ K}

V=0.05 \text{ m}^3

. Find pressure (

R=8.31

Example 2

easy

Convert

27^\circ\text{C}

to kelvin for use in the gas law.

Example 3

easy

At constant temperature, a gas at

100000 \text{ Pa}

and

2 \text{ m}^3

is compressed to

1 \text{ m}^3

. Find the new pressure.

Example 4

easy

At constant pressure, a gas at

300 \text{ K}

occupies

0.6 \text{ m}^3

. Heated to

600 \text{ K}

, find the new volume.

Example 5

easy

How many moles of gas occupy

V=0.0249 \text{ m}^3

P=100000 \text{ Pa}

and

T=300 \text{ K}

? (

R=8.31

)

Example 6

easy

At constant volume, a gas at

300 \text{ K}

and

100000 \text{ Pa}

is heated to

450 \text{ K}

. Find the new pressure.

Example 7

easy

PV = nRT

, what happens to pressure if you double the number of moles at fixed

V

and

T

Example 8

easy

A gas at

100000 \text{ Pa}

0.02 \text{ m}^3

250 \text{ K}

is heated to

500 \text{ K}

at constant volume. Find the new pressure.

Example 9

medium

A gas at

P_1=120000 \text{ Pa}

V_1=0.4 \text{ m}^3

T_1=300 \text{ K}

changes to

V_2=0.2 \text{ m}^3

T_2=450 \text{ K}

. Find

P_2

Example 10

medium

Find the volume of

3 \text{ mol}

of gas at

400 \text{ K}

and

200000 \text{ Pa}

. (

R=8.31

)

Example 11

medium

A sealed rigid tank of gas at

300 \text{ K}

reads

150000 \text{ Pa}

. On a hot day it reaches

360 \text{ K}

. Find the new pressure.

Example 12

medium

A balloon at

0.002 \text{ m}^3

and

100000 \text{ Pa}

rises to where pressure is

80000 \text{ Pa}

at the same temperature. Find the new volume.

Example 13

medium

How many moles are in

0.0224 \text{ m}^3

of gas at

273 \text{ K}

and

101325 \text{ Pa}

? (

R=8.31

)

Example 14

medium

A gas does work expanding from

0.01 \text{ m}^3

0.03 \text{ m}^3

at constant pressure

200000 \text{ Pa}

. Find the work done by the gas.

Example 15

medium

At constant pressure and moles, a gas is heated from

250 \text{ K}

400 \text{ K}

. Its volume becomes

0.8 \text{ m}^3

. Find the original volume.

Example 16

medium

A gas at

300 \text{ K}

and

0.6 \text{ m}^3

is heated at constant pressure until it occupies

1.0 \text{ m}^3

. Find the new temperature.

Example 17

medium

Find the temperature of

2 \text{ mol}

of gas at

150000 \text{ Pa}

0.04 \text{ m}^3

. (

R=8.31

)

Example 18

challenge

0.05 \text{ m}^3

tank holds gas at

300 \text{ K}

and

200000 \text{ Pa}

. Half the gas leaks out at constant temperature. Find the new pressure.

Example 19

challenge

Two tanks,

0.02 \text{ m}^3

300000 \text{ Pa}

and

0.03 \text{ m}^3

100000 \text{ Pa}

, both at the same temperature, are connected. Find the final pressure.

Example 20

challenge

A gas at

0.04 \text{ m}^3

250000 \text{ Pa}

300 \text{ K}

is compressed to

0.01 \text{ m}^3

and cooled to

200 \text{ K}

. Find the final pressure.

Example 21

easy

Convert

-23^\circ\text{C}

to kelvin for use in

PV=nRT

Example 22

easy

A gas has

n=0.5 \text{ mol}

T=400 \text{ K}

V=0.02 \text{ m}^3

. Find pressure (

R=8.31

Example 23

easy

At constant temperature, a gas at

50000 \text{ Pa}

and

4 \text{ m}^3

is compressed to

2 \text{ m}^3

. Find the new pressure.

Example 24

easy

At constant pressure, a gas at

200 \text{ K}

occupies

0.3 \text{ m}^3

. Cooled to

100 \text{ K}

, find the new volume.

Example 25

easy

How many moles of gas occupy

V=0.01 \text{ m}^3

P=300000 \text{ Pa}

and

T=300 \text{ K}

? (

R=8.31

)

Example 26

easy

Convert

77^\circ\text{C}

to kelvin.

Example 27

medium

Find the volume of

0.5 \text{ mol}

of gas at

500 \text{ K}

and

50000 \text{ Pa}

. (

R=8.31

)

Example 28

medium

A sealed rigid bottle at

290 \text{ K}

reads

200000 \text{ Pa}

. In the sun it warms to

348 \text{ K}

. Find the new pressure.

Example 29

medium

A weather balloon at

0.005 \text{ m}^3

100000 \text{ Pa}

290 \text{ K}

rises to

40000 \text{ Pa}

and

232 \text{ K}

. Find

V_2

Example 30

medium

Find the temperature of

4 \text{ mol}

of gas at

100000 \text{ Pa}

0.1 \text{ m}^3

. (

R=8.31

)

Example 31

medium

At constant pressure and moles, a gas at

T_1=200 \text{ K}

has

V_1=0.3 \text{ m}^3

. Find its volume at

T_2=500 \text{ K}

Example 32

medium

A gas at

250 \text{ K}

and

0.8 \text{ m}^3

is heated at constant pressure until it occupies

1.2 \text{ m}^3

. Find

T_2

Example 33

medium

2 \text{ mol}

of gas at

300 \text{ K}

is sealed in a rigid

0.05 \text{ m}^3

tank. Find

P

. (

R=8.31

)

Example 34

hard

3 \text{ mol}

of gas occupies

0.06 \text{ m}^3

250000 \text{ Pa}

. Find

T

. (

R=8.31

)

Example 35

hard

Two rigid tanks at the same temperature: tank A (

0.01 \text{ m}^3

500000 \text{ Pa}

) and tank B (

0.04 \text{ m}^3

100000 \text{ Pa}

). A valve is opened. Find the final pressure.

Example 36

hard

A bicycle pump compresses

0.0006 \text{ m}^3

of air at

100000 \text{ Pa}

300 \text{ K}

into a tire so the gas ends at

0.0002 \text{ m}^3

and

350 \text{ K}

. Find the new pressure.

Example 37

hard

An empty

0.025 \text{ m}^3

cylinder is filled with

4 \text{ mol}

of nitrogen at

293 \text{ K}

. Find the gauge pressure if atmospheric pressure is

101325 \text{ Pa}

. (

R=8.31

)

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Related Concepts

Pressure Temperature

Background Knowledge

These ideas may be useful before you work through the harder examples.

pressuretemperature