Question

A balloon initially has a volume of 45 L at sea level, where temperature is 25∘C and the pressure is 1.0 atm. It rises to an elevation of 2.0 km, where the temperature is 5.0∘C and the pressure is 0.78 atm. What is the balloon's volume at this height?

Answer 1

53.8 L

Explanation:

We can use the ideal gas formula that relates pressure, volume and temperature:

`(P_1 V_1)/(T_1) = (P_2 V_2)/(T_2)`

where P1 = initial pressure = 1.0 atm

V1 = initial volume = 45 L

T1 = initial temperature = 25°C = 25 + 273 = 298 K

P2 = final pressure = 0.78 atm

V2 = final volume

T2 = final temperature = 5.0°C = 5 + 273 = 278 K

Therefore, the final volume will be:

`(1 * 45)/(298) = (0.78 * V_2)/(278)\\\\0.151 = 0.002806 V_2\\\\=> V_2 = 0.151 / 0.002806\\\\V_2 = 53.8 L`

Its volume is 53.8 L