# Charles law formula

The Charles’s law formula, which is expressed as V1/T1 = V2/T2, relates the volume and temperature of a gas. In this formula, V1 and T1 represent the initial volume and temperature of the gas, while V2 and T2 represent the final volume and temperature, respectively. This formula can be used to calculate the volume or temperature of a gas under different conditions, given the initial volume and temperature of the gas.

Contents

## Practice problems

### Problem #1

A rubber ball contains 2 L of hydrogen gas at an initial temperature of 10 ℃. Calculate the final volume of the gas if the temperature is increased to 90 ℃, according to Charles’s law.

Solution

Given data:

• Initial volume of the gas, V1 = 2 L
• Initial temperature of the gas, T1 = 10 ℃ = 283 K
• Final volume of the gas, V2 = ?
• Final temperature of the gas, T2 = 90 ℃ = 363 K

Applying the formula:

• V1/T1 = V2/T2
• V2 = (V1 × T2) ÷ T1
• V2 = (2 × 363) ÷ 283
• V2 = 726 ÷ 283
• V2 = 2.56 L

Therefore, the final volume of the gas is 2.56 L.

### Problem #2

A rubber ball is filled with 3 L of helium gas at a temperature of 12 ℃. If the volume of the gas changes to 4 L, what is the final temperature of the gas?

Solution

Given data:

• Initial volume of the gas, V1 = 3 L
• Initial temperature of the gas, T1 = 12 ℃ = 285 K
• Final volume of the gas, V2 = 4 L
• Final temperature of the gas, T2 = ?

Applying the formula:

• V1/T1 = V2/T2
• T2 = (V2 × T1) ÷ V1
• T2 = (4 × 285) ÷ 3
• T2 = 1140 ÷ 3
• T2 = 380 K = 107 ℃

Therefore, the final temperature of the gas is 107 ℃.

### Problem #3

A container is filled with a few liters of hydrogen gas at an initial temperature of 20 ℃. If the final volume of the gas is 8 L at a final temperature of 50 ℃, then what was the initial volume of the gas according to Charles’s law?

Solution

Given data:

• Initial temperature of the gas, T1 = 20 ℃ = 293 K
• Final volume of the gas, V2 = 8 L
• Final temperature of the gas, T2 = 50 ℃ = 323 K
• Initial volume of the gas, V1 = ?

Applying the formula:

• V1/T1 = V2/T2
• V1 = (V2 × T1) ÷ T2
• V1 = (8 × 293) ÷ 323
• V1 = 2344 ÷ 323
• V1 = 7.25 L

Therefore, the initial volume of the gas is 7.25 L.

### Problem #4

One box containing 4 L of argon gas is heated at an initial temperature. If the final temperature of the gas is 180 ℃ and the final volume of the gas is 6 L, then calculate the initial temperature of the gas.

Solution

Given data:

• Initial volume of the gas, V1 = 4 L
• Final temperature of the gas, T2 = 180 ℃ = 453 K
• Final volume of the gas, V2 = 6 L
• Initial temperature of the gas, T1 = ?

Applying the formula:

• V1/T1 = V2/T2
• T1 = (V1 × T2) ÷ V2
• T1 = (4 × 453) ÷ 6
• T1 = 1812 ÷ 6
• T1 = 302 K = 29 ℃

Therefore, the initial temperature of the gas is 29 ℃.