Question

A weather balloon is inflated to a volume of 27.6 L at a pressure of 755 mmHg and a temperature of 29.9 ∘C. The balloon rises in the atmosphere to an altitude where the pressure is 385 mmHg and the temperature is -14.1 ∘C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Answer 1

Answer: The volume of the balloon at this altitude is 46.3 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 = 755 mm Hg

$P_2$ = final pressure of gas (at STP) = 385 mm Hg

$V_1$ = initial volume of gas = 27.6 L

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $29.9^0C=(29.9+273)K=302.9K$

$T_2$ = final temperature of gas = $-14.1^0C=((-14.1)+273)K=258.9K$

Putting all the values we get:

$\frac{755\times 27.6}{302.9}=\frac{385\times V_2}{258.9}$

$V_2=46.3L$

Thus the volume of the balloon at this altitude is 46.3 L