Answer to Question #191588 in Electricity and Magnetism for Bonna

Question

A weather balloon contains 12.0 m3 of hydrogen gas when the balloon is released from a location at which the temperature is 22.0◦C and the pressure is 101kPa. The balloon rises to a location where the temperature is −30.0◦C and the pressure is 20.0 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

Answer 1

ideal gas equation , we can say

PV = nRT

P = pressure

V = volume

n = number of moles

R = avagadro gas constant

T = temperature

we can write from above

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

$\frac{101\times12}{273+22}=\frac{20\times V_2}{273-3-}$

$V_2=50m^3$

So from above expression we can see that for constant number of moles we can say

So finally the volume will be 50 m³