The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is

The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is
  1. $1: 7$
  2. $5: 7$
  3. $3: 7$
  4. $2: 7$

Solution

For monoatomic gas, $\mathrm{f}=3$ $\therefore\left(\mathrm{C}_{\mathrm{p}}\right)_1=\left(1+\frac{\mathrm{f}}{2}\right) \mathrm{R}=\left(1+\frac{3}{2}\right) \dot{\mathrm{R}}=\frac{5 \mathrm{R}}{2}$ For diatomic gas, $\mathrm{f}=5$ $\begin{aligned} & \therefore\left(\mathrm{C}_{\mathrm{p}}\right)_2=\left(1+\frac{\mathrm{f}}{2}\right) \mathrm{R}=\left(1+\frac{5}{2}\right) \mathrm{R}=\frac{7 \mathrm{R}}{2} \\ & \therefore \frac{\left(\mathrm{C}_{\mathrm{p}}\right)_1}{\left(\mathrm{C}_{\mathrm{p}}\right)_2}=\frac{\frac{5 \mathrm{R}}{2}}{\frac{7 \mathrm{R}}{2}}=5: 7 \end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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