Question

Relating Pressure, Volume, Amount, and Temperature: The ideal Gas LawA high altitude balloon is filled with 1.41 × 104 L of hydrogen at a temperature of 21 °C and a pressure of 745 torr. What is the volume of the balloon at a height of 20 km, where the temperature is –48 °C and the pressure is 63.1 torr?

Answer 1

Answer: The volume of balloon at a height of 20 km is $1.32\times 10^5L$

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:

$P_1=745torr\\V_1=1.41\times 10^4L\\T_1=21^oC=[21+273]K=294K\\P_2=63.1torr\\V_2=?L\\T_2=-40^oC=[-40+273]K=233K$

Putting values in above equation, we get:

$\frac{745torr\times 1.41\times 10^4L}{294K}=\frac{63.1torr\times V_2}{233K}\\\\V_2=\frac{745\times 1.41\times 233}{294\times 63.1}=1.32\times 10^5L$

Hence, the volume of balloon at a height of 20 km is $1.32\times 10^5L$