Question

A box contains 104 gas molecules, 2500 of nitrogen and 7500 of argon in thermal equilibrium. The molecular weight of N2 is 28g/mol, and of Ar is 40g/mol. The total thermal energy of the collection of 104 molecules is 5x10-17J. What is the temperature of this gas

Answer 1

Answer : The temperature of this gas will be, 206.9 K

Explanation :

The expression for the kinetic energy per molecule of monoatomic gas (argon) is:

$K.E_{argon}=n_{argon}\times \frac{3}{2}\times K_BT$      ...........(1)

The expression for the kinetic energy per molecule of diatomic gas (nitrogen gas) is:

$K.E_{nitrogen}=n_{nitrogen}\times \frac{5}{2}\times K_BT$      .............(2)

The total kinetic energy of the molecule will be,

$K.E_{Total}=K.E_{argon}+K.E_{nitrogen}$

Now put all the expression in this, we get:

$K.E_{Total}=(7500)\times \frac{3}{2}\times K_BT+(2500)\times \frac{5}{2}\times K_BT$

$T=\frac{K.E}{17500\times K_B}$

Now put all the given values in this expression, we get:

$T=\frac{5\times 10^{-17}J}{17500\times (1.381\times 10^{-23}J/K)}$

$T=206.9K$

Therefore, the temperature of this gas will be, 206.9 K