Question

A hot air balloonist puts 52000 L of air into their balloon at 500 Celsius and 975 atm. When they heat
the air to 750 celsius what is the final volume (in cm^3) in the balloon?

Answer 1

Answer: The final volume in the balloon is $68.818cm^3$    

Explanation:

Charles' Law states that volume is directly proportional to the temperature of the gas at constant pressure and number of moles of gas.

Mathematically,

$\text{Volume}\propto \text{Temperature}$

Or,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$   (At constant pressure and number of moles)

$V_1$ = initial volume = 52000 L

$V_2$ = final volume = ?

$T_1$ = initial temperature = $500^0C=(500+273)K=773 K$

$T_2$ =  final temperature = $750^0C=(750+273)K=1023 K$

$\frac{52000}{773}=\frac{V_2}{1023}$

$V_2=68818L=68.818ml=68.818cm^3$       $(1L=1000ml=1000cm^3)$

Thus final volume in the balloon is $68.818cm^3$