Question

The value of $\gamma$ on monoatomic, diatomic and triatomic gases is ___, ___ and ___ respectively.

• A. 1.66, 1.40, 1.33
• B. 1.33, 1.40, 1.66
• C. 2, 1.66, 1.5
• D. None of these

Answer 1

The correct option is (B)

Gamma is defined as the ratio of specific heat at constant pressure to the specific heat at constant volume.

$\gamma =\frac{C_P}{C_V}$

$C_P$ and $C_V$ are specific heat capacities at constant pressure and volume respectively.

Part 1: Monoatomic gas

For monoatomic gas, $N=1$

The total degree of freedom $=3$

$C_V=\frac{3R}{2}$

Since $C_P=C_V+R$

$C_P=\frac{3R}{2}+R$

$C_P=\frac{5R}{2}$

$\gamma =\frac{\frac{5R}{2}}{\frac{3R}{2}}$

$\gamma =\frac{5}{3}=1.66$

Part 2: Diatomic gas

For diatomic gas, $N=2$

The total degree of freedom $=5$

$C_V=\frac{5R}{2}$

$C_P=\frac{7R}{2}$

$\gamma =\frac{\frac{7R}{2}}{\frac{5R}{2}}$

$\gamma =\frac{7}{5}=1.40$

Part 3: Triatomic gas

For triaomic gas, $N=3$

The total degree of freedom $=7$

$C_V=\frac{7R}{2}$

$C_P=\frac{9R}{2}$

$\gamma =\frac{\frac{9R}{2}}{\frac{7R}{2}}$

$\gamma =\frac{9}{7}=1.33$