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)* (3)/(2)* K_BT` ...........(1)

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

`K.E_(nitrogen)=n_(nitrogen)* (5)/(2)* 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)* (3)/(2)* K_BT+(2500)* (5)/(2)* K_BT`

`T=(K.E)/(17500* K_B)`

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

`T=(5* 10^(-17)J)/(17500* (1.381* 10^(-23)J/K))`

`T=206.9K`

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