If $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{V}}$ denote the specific heats (per unit mass) of an…

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.
  1. $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}^2}$
  2. $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$
  3. $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}}$
  4. $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{MR}$

Solution

$\begin{array}{r} \mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R} \\ \therefore \quad \mathrm{Mc}_{\mathrm{p}}-\mathrm{MC}_{\mathrm{V}}=\mathrm{R} \\ \mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}} \end{array}$ .

Asked in: NEET 2010 (Mains)

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