The molar specific heat capacity of a diatomic gas at constant pressure is C . The molar specific heat…

The molar specific heat capacity of a diatomic gas at constant pressure is C . The molar specific heat capacity of a monoatomic gas at constant volume is
  1. $\frac{2 \mathrm{C}}{7}$
  2. $\frac{3 \mathrm{C}}{7}$
  3. $\frac{\mathrm{C}}{7}$
  4. $\frac{4 \mathrm{C}}{7}$

Solution

For diatomic gas, $\mathrm{f}_1=5$ $C_{v_1}=\frac{f_1 R}{2}=\frac{5 R}{2}$ $C_{p_1}=C_v+R=\frac{5 R}{2}+R \frac{7 R}{2}=C$ For monoatomic gas, $\mathrm{f}_2=3$ $C_{v_2}=\frac{f_2 R}{2}=\frac{3 R}{2}$ Now, $\frac{\mathrm{C}}{\mathrm{C}_{\mathrm{v}_2}}=\frac{\frac{7 \mathrm{R}}{2}}{\frac{3 \mathrm{R}}{2}}=\frac{7}{3}$ $\therefore C_{v_2}=\frac{3 C}{7}$

Asked in: AP EAMCET 2024 (18 May Shift 1)

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