Question

A gas-filled balloon having a volume of 3.60 L at 1.15 atm and 20°C is allowed to rise to the stratosphere (about 30 km above the surface of the Earth), where the temperature and pressure are −50°C and 5.40 × 10−3 atm, respectively. Calculate the final volume of the balloon.

Answer 1

Answer: The new volume of the balloon will be 583.5 L

Explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law.

The equation follows:

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

where,

$P_1,V_1\text{ and }T_1$ are the initial pressure, volume and temperature of the gas

$P_2,V_2\text{ and }T_2$ are the final pressure, volume and temperature of the gas

We are given:

$P_1=1.15atm\\V_1=3.60L\\T_1=20^oC=[20+273]K=293K\\P_2=5.40\times 10^{-3}atm=0.00540atm\\V_2=?\\T_2=-50^oC=[-50+273]K=223K$

Putting values in above equation, we get:

$\frac{1.15atm\times 3.60L}{293K}=\frac{0.00540atm\times V_2}{223K}\\\\V_2=\frac{1.15\times 3.60\times 223}{293\times 0.00540}=583.5L$

Hence, the new volume of the balloon will be 583.5 L