Q68 / 120 · NEET 2010 (Mains) · Physics
If $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{V}}$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$
where $R$ is the molar gas constant.
- A$\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}^2}$
- B$\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$
- Correct answerC$\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}}$
- D$\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{MR}$
Solution
$$
\begin{array}{r}
\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R} \\
\therefore \quad \mathrm{Mc}_{\mathrm{p}}-\mathrm{MC}_{\mathrm{V}}=\mathrm{R} \\
\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}}
\end{array}
$$
Hence, the correct answer is option: 'C'.