## Introduction

The general gas law in physics is the combination of Boyle’s, Charle’s, and Pressure laws for an ideal gas.

We can write the formula as

PV / T = Constant

Where

P = pressure

V = volume

T = Temperature

And because of the constant, we can now write the formula as

P_{1}V_{1} / T_{1} = P_{2}V_{2} / T_{2}

## General Gas Law in Physics Practice Problems

Here are a few examples to help you understand how to apply the formula for general gas law and calculate a problem.

### Problem 1

A mass of gas at 17^{0}c and 700mmHg has a volume of 1.2m^{3}. Determine its volume at 27^{0}c and pressure at 750 mmHg?

#### Answer

Solution: To calculate the volume from general gas law, we need to first extract our data from the question

Data:

Initial Pressure = P_{1 }= 700mmHg

Final Pressure = P_{2 }= 700mmHg

Initial Temperature = T_{1 }= 17^{0}c = 273 + 17 = 290

Final Temperature = T_{2 }= 27^{0}c = 273 + 27 = 300

Additionally, initial Volume = V_{1 }= 1.2m^{3}

Also, Initial Volume = V_{1 }= ?

Using the general gas law,

( P_{1 }V_{1}) / ( T` _{1}` )= ( P

_{2 }V

_{2}) / ( T

_{2})

By Making V_{2} subject of the formula,we have

_{ }Thus, V_{2} = ( P_{1 }V_{1}T_{2}) / (P_{2} T` _{1}` )

by substituting the above expression with our data, we have:

Final volume, V_{2} = ( 700 x 1.2 x 300 ) / ( 750 x 290 )

Therefore, V_{2} = ( 252,000 ) / ( 217,500 )

This will give us our final answer as V_{2} = 1.156m^{3}

Therefore, the final volume is 1.2m^{3}

### Problem 2

The volume and pressure of a given mass of gas at 27^{0}C are 76 cm^{3} and 80 cm of mercury respectively. Calculate its volume at standard temperature and pressure (s.t.p)

#### Answer

**Data**

The original volume, V_{1} = 76 cm^{3}

Initial pressure, P_{1 } = 80 cmHg

Final pressure, P_{2} = 760 cmHg [Because of the standard temperature and pressure]

The initial temperature, T` _{1}` = 27

^{0}C = 27 + 273 = 300 k

Final temperature, T` _{2}` = 273k [Because of the standard temperature and pressure]

**Unknown**

The final volume, V_{2} = ?

**Formula**

We will now apply our formula to solve the problem

( P_{1 }V_{1}) / ( T` _{1}` )= ( P

_{2 }V

_{2}) / ( T

_{2})

after inserting our data, we will now have

(80 x 76) / (300) = (76 x V_{2}) / 273

By making V_{2} subject of the formula, we will obtain our answer as

**V _{2} = 72.8 cm^{3} **

### Problem 3

A given mass of an ideal gas occupies a volume V at a temperature T and under a pressure P. If the pressure is increased to 2P and the temperature reduced to (1/2)T, then what is the percentage change in the volume of the gas?

#### Answer

**The final answer to the above question is 75%**

**Explanation**

Since we have a formula that says P_{1}V_{1} / T_{1} = P_{2}V_{2} / T_{2}

and

V_{1} = V

P_{1} = P

P_{2} = 2P

T_{1} = T

T_{2} = (1/2)T

V_{2} = ?

We can make V_{2} subject of the formula and interpret it as

V_{2} = (P x V x (1/2)T ) / (2P x T)

And we will have

V_{2} = (1/2)V / 2 = 0.25 V

The percentage change in volume will now become

[(V_{1} – V_{2}) / V_{1} ] x 100%

Which will now be

[(V – 0.25V) / V ] x 100%

hence

[0.75V / V ] x 100% = 0.75 x 100% = 75%

**Therefore, the percentage change in the volume of the gas is 75%**

### Problem 4

The pressure of a given mass of a gas changes from 300 Nm^{-2} to 120 Nm^{-2} while the temperature drops from 127^{0}C to -73^{0}C. What is the ratio of the final volume to the initial volume?

#### Answer

**The final answer to the question is V _{1} : V_{2} = 5 : 4**

**Explanation**

P_{1} = 300 Nm^{-2}

and P_{2} = 120 Nm^{-2}

T_{1} = 127 + 273 = 400 K

we have T_{2} = -73 + 273 = 200 K

**Formula**

The formula we will use is P_{1}V_{1} / T_{1} = P_{2}V_{2} / T_{2}

**Solution**

We will now insert our data into the formula

(300 x V_{1}) / 400 = (120 x V_{2}) / 200

To have a ratio of V_{1} to V_{2}

Hence,

**V _{2} : V_{1} = 60000 / 48000**

60 / 48 = V_{2} / V_{1}

When we divide both 60 and 48 by 12, we will obtain

**V _{2} / V_{1} = 5 / 4**

*You may also like to read:*

How to Calculate Cubic Expansivity with Examples

Linear Expansivity: Definition and Calculations

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