Let's assume that both He and N₂ have ideal gas behavior.
Then we can use ideal gas law,
PV = nRT
Where, P is the pressure of gas, V is the volume,
n is moles of gas, R is universal gas constant and T is the temperature in
Kelvin.
The P and V are same for the
both gases.
R is a
constant.
The only variables are n and T.
Let's say temperature of He is T₁ and temperature of N₂ is T₂.
n = m/M where n is
moles, m is mass and M is molar mass.
Molar mass of He is 4 g/mol and molar mass of N₂ is 28 g/mol
Since mass (m) of both gases are same,
moles of He = m/4
moles of N₂ = m/28
Let's apply the ideal gas equation for both gases.
For He gas,
PV = (m/4)RT₁ (1)
For N₂ gas,
PV = (m/28)RT₂ (2)
(1) = (2)
(m/4)RT₁ =
(m/28)RT₂
T₁/4
= T₂/28
T₁ = T₂/7
7T₁ = T₂
Hence, the
temperature of N₂ gas is higher by 7
times than the temperature of He gas.
