Question

Three moles of nitrogen is mixed with six moles of helium. The effective molar specific heat of the mixture at constant volume is A) 1.7 R B) 1.4 R C) 1.83 R D) 1.65 R​

Answer 1

The effective molar specific heat of the mixture at constant volume is 1.83R

Therefore, option (C) is correct.

Explanation:

Given:

3 moles of Nitrogen is mixed with 6 moles of Helium

To find out:

The effective molar specific heat of the mixture at constant volume

Solution:

The molar specific heat capacity of a gas at constant volume is the amount of heat required to raise the temperature of 1 mol of the gas by 1°C

at the constant volume.

or, $C_v=\frac{n_1C_{v1}+n_2C_{v2}}{n_1+n_2}$

Given that

$n_1=3$ and $n_2=6$

Nitrogen (N₂) is a diatomic gas

Therefore, $C_{v1}=\frac{5}{2}R$

Helium (He) is a monoatomic gas

Thus, $C_{v2}=\frac{3}{2}R$

Therefore,

$C_v=\frac{3\times(5R/2)+6\times (3R/2)}{3+6}$

$\implies C_v=\frac{33R/2}{9}$

$\implies C_v=\frac{33}{18}R$

$\implies C_v=1.83R$

Hope this answer is helpful.