Question

If 1 mole of a monoatomic gas (=5/3) is mixed with one mole of diatomic gas (=7/5) , the value of for the mixture is:

• A. 1.4
• B. 1.5
• C. 1.65
• D. 3.07

Answer 1

Answer: (B)

1.5

For monoatomic gas, $C_V=\frac{3}{2}RT$ and $C_P=\frac{5}{2}RT$

For diatomic gas, $C_V=\frac{5}{2}RT$ and $C_P=\frac{7}{2}RT$

Thus for mixture of $1$ mole each,

$C_V=\frac{\frac{3}{2}RT+\frac{5}{2}RT}{2}=\frac{\frac{8}{2}RT}{2}$

$C_P=\frac{\frac{5}{2}RT+\frac{7}{2}RT}{2}=\frac{\frac{12}{2}RT}{2}$

$\therefore$ $\gamma$ for mixture $=\frac{C_P}{C_V}=\frac{3}{2}\frac{RT}{RT}=1.5$

$\therefore$ Correct answer is $B\left(1.50\right)$.