Q32 / 180 · JIPMER 2019 · Chemistry

What is the value of $\gamma$ for mono atomic gas (ideal gas)?

  • A
    $\frac{7}{5}$
  • B
    $\frac{4}{3}$
  • C
    $\frac{5}{2}$
  • Correct answer
    D
    None of these

Solution

Key Idea $\gamma=\mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}$ where, $\mathrm{C}_{\mathrm{P}}$ and $\mathrm{C}_{\mathrm{v}}$ are heat capacities at constant pressure and volume, respectively. For monoatomic gas, $\mathrm{C}_{\mathrm{P}}=5 \mathrm{cal}, \mathrm{C}_{\mathrm{V}}=3 \mathrm{cal}$ $\gamma=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}=1.67$ For diatomic gas, $\mathrm{C}_{\mathrm{P}}=7 \mathrm{cal}, \mathrm{C}_{\mathrm{V}}=5 \mathrm{cal}$ $_{\mathrm{V}}=6 \mathrm{cal}$ $\gamma=\frac{C_P}{C_V}=\frac{8}{6}=1.33$

Hence, the correct answer is option: 'D'.

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