First slide

Internal energy

Question

One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is

Moderate

A

8
B

$\frac{3}{2} R$
C

2R
D

2.5R

Solution

$\begin{array}{l} {(C_{V})}_{mix} = \frac{μ_{1} C_{V_{1}} + μ_{2} C_{V_{2}}}{μ_{1} + μ_{2}} = \frac{1 \times \frac{3}{2} R + 1 \times \frac{5}{2} R}{1 + 1} = 2 R \\ ({(C_{V})}_{mono} = \frac{3}{2} R, {(C_{V})}_{di} = \frac{5}{2} R) \end{array}$

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