Question

A weather balloon is inflated to a volume of 28.6 L at a pressure of 737 mmHg and a temperature of 26.8 ∘C. The balloon rises in the atmosphere to an altitude where the pressure is 385 mmHg and the temperature is -16.3 ∘C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Answer 1

Answer: Volume of the balloon at this altitude is 46.9 L

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 = 737 mm Hg

$P_2$ = final pressure of gas =  385 mm Hg

$V_1$ = initial volume of gas = 28.6 L

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $26.8^oC=273+26.8=299.8K$

$T_2$ = final temperature of gas = $-16.3^oC=273-16.3=256.7K$

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

$\frac{737\times 28.6}{299.8}=\frac{385\times V_2}{256.7}$

$V_2=46.9L$

Thus the volume of the balloon at this altitude is 46.9 L