Q138 / 150 · MHT CET 2024 (16 May Shift 2) · Physics

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is

  • A
    $30 \%$
  • B
    $40 \%$
  • C
    $50 \%$
  • Correct answer
    D
    $60 \%$

Solution

For a monoatomic gas, $\gamma=\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}$ We know $\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}$ and $\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$ $\frac{\Delta U=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{~T}}{\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{~T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}=\frac{3}{5}$ $\therefore \quad$ The percentage of total heat used in changing the internal energy is $\frac{3}{5} \times 100=60 \%$.

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

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