Here is an example of an ideal gas problem where the pressure of the gas is held constant.

### Question

A balloon filled with an ideal gas at a temperature of 27 °C at 1 atm of pressure. If the balloon is heated to 127 °C at constant pressure, by what factor does the volume change?

### Solution

Step 1

Charles' Law states

V_{i} / T_{i} = V_{f} / T_{f} where

V_{i} = initial volume

T_{i} = initial temperature

V_{f} = final volume

T_{f} = final temperature

**Step 1**

Convert temperatures to Kelvin

K = °C + 273

T_{i} = 27 °C + 273

T_{i} = 300 K

T_{f} = 127 °C + 273

T_{f} = 400 K

**Step 2**

Solve Charles' Law for V_{f}

V_{f} = ( V_{i} / T_{i} ) / T_{f}

Rearrange to show final volume as a multiple of initial volume

V_{f} = ( T_{f} / T_{i} ) x V_{i}

V_{f} = ( 400 K / 300 K) x V_{i}

V_{f} = 4/3 V_{i}

### Answer:

The volume changes by a factor of 4/3.