Kinetic Theory of Gases and Radiation — Physics STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsKinetic Theory of Gases and Radiation3 Marks
Question
Express Mayer's relation in terms of the principal specific heats, $S_p$ and $S_V$.
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Answer
Mayer's relation: $C_p-C_V=R$. Let $M_0=$ molar mass of the gas, $S_p=$ specific heat of the gas at constant pressure and $\mathrm{S}_{\mathrm{V}}=$ specific heat of the gas at constant volume. Now, $C_p=M_0 S_p$ and $C_V=M_0 S_V$ $\therefore \mathrm{M}_0 \mathrm{~S}_{\mathrm{p}}-\mathrm{M}_0 \mathrm{~S}_{\mathrm{V}}=\mathrm{R}$ $\therefore \mathrm{S}_{\mathrm{p}}-\mathrm{S}_{\mathrm{V}}=\frac{R}{M_0}$ when heat and work are expressed in the same units. If heat is expressed in calorie or kilo calorie and work is expressed in erg or joule, we get, $\mathrm{S}_{\mathrm{p}}-\mathrm{S}_{\mathrm{v}}=\frac{R}{M_0 \cdot J}$, where $\mathrm{J}$ is the mechanical equivalent of heat. [Notes : $C_p=\frac{1}{n} \cdot \frac{d Q_p}{d T}$ and $S_p=\frac{1}{M} \cdot \frac{d Q_p}{d T}$ $\therefore \frac{C_P}{S_P}=\frac{M}{n}=\frac{n M_0}{n}=M_0$
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