Question

A gas mixture contains monoatomic and diatomic molecules of 2 moles each. The mixture has a total internal energy of (symbols have usual meanings) (A) 3 RT (B) 5 RT 4 (C) 8 RT (D) 9 RT​

Answer 1

Answer:

11 rt

Explanation:

For two moles of diatomic oxygen with no vibrational mode.

U  

1

​

=2×  

2

5

​

RT=5RT

For four moles of monoatomic Argon,

U  

2

​

=4×  

2

3

​

RT=6RT

∴u=u  

1

​

+u  

1

​

=5RT+6RT=11RT

Answer 2

Given info : A gas mixture contains monoatomic and diatomic molecules of 2 moles each.

To find : the mixture has a total internal energy of (symbol have usual meanings )

solution : first we have to find the molar capacity at constant volume of mixture.

molar capacity at constant volume of monoatomic molecules, C₁ = 3R/2

molar capacity at constant volume of monoatomic molecules, C₂ = 5R/2

now, molar capacity of mixture,C = (n₁C₁ + n₂C₂)/(n₁ + n₂)

                                                      = (2 × 3R/2 + 2 × 5R/2)/4 = 2R

now total internal energy of the mixture = (n₁ + n₂)CRT = 4(2R)T = 8RT

therefore the internal energy of the mixture is 8RT.