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`

Step-by-step 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,

`(V_1)/(T_1)=(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`

`(52000)/(773)=(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`