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* 10^5L`

Step-by-step explanation:

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

`(P_1V_1)/(T_1)=(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* 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:

`(745torr* 1.41* 10^4L)/(294K)=(63.1torr* V_2)/(233K)\\\\V_2=(745* 1.41* 233)/(294* 63.1)=1.32* 10^5L`

Hence, the volume of balloon at a height of 20 km is
`1.32* 10^5L`