Question

A 4.0L weather balloon is launched from sea level where the temperature is 25°C. It rises to an altitude where the pressure is 0.05atm and the temperature is -75°C. If the balloon has the capacity to expand to a 50 liter volume before bursting, will the balloon survive?

Answer 1

Answer: The balloon will not survive.

Explanation:

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1$ = initial pressure of gas =  1 atm

$P_2$ = final pressure of gas = 0.05 atm

$V_1$ = initial volume of gas = 4.0 L

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $25^oC=273+25=298K$

$T_2$ = final temperature of gas = $-75^oC=273-75=198K$

Now put all the given values in the above equation, we get:

$\frac{1\times 4.0}{298}=\frac{0.05\times V_2}{198}$

$V_2=53.2L$

As the balloon has the capacity to expand to a 50 liter volume before bursting, it can not survive as it occupies volume higher than 50 L