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
Vi / Ti = Vf / Tf where
Vi = initial volume
Ti = initial temperature
Vf = final volume
Tf = final temperature
Step 1
Convert temperatures to Kelvin
K = °C + 273
Ti = 27 °C + 273
Ti = 300 K
Tf = 127 °C + 273
Tf = 400 K
Step 2
Solve Charles' Law for Vf
Vf = ( Vi / Ti ) / Tf
Rearrange to show final volume as a multiple of initial volume
Vf = ( Tf / Ti ) x Vi
Vf = ( 400 K / 300 K) x Vi
Vf = 4/3 Vi
Solution
The volume changes by a factor of 4/3.
