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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Kinetic Theory of Gases

NEET 2010 · Physics · Kinetic Theory of Gases

If C_ p and C_ V denote the specific heats (per unit mass) of an...

If Cp\mathrm{C}_{\mathrm{p}} and CV\mathrm{C}_{\mathrm{V}} denote the specific heats (per unit mass) of an ideal gas of molecular weight MM where RR is the molar gas constant.

Options

  1. ACp−CV=RM2\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}^2}
  2. BCp−CV=R\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}
  3. CCp−CV=RM\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}}
  4. DCp−CV=MR\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\mathrm{MR}

Correct answer

C. Cp−CV=RM\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{M}}

Step-by-step solution

Cp−CV=R∴Mcp−MCV=RCp−CV=RM\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}$$
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