Question

You have two containers of equal volume. one is full of helium gas. the other holds an equal mass of nitrogen gas both gases have the same pressure how does thegas. bothgaseshavethesamepressure. howdoesthetemperature of the helium compare to the temperature of the nitrogen?

Answer 1

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.