Q138 / 160 · AP EAMCET 2023 (18 May Shift 2) · Physics

A diatomic gas has an initial internal energy of $80 \mathrm{cal}$. A work of $18 \mathrm{cal}$ is done on the gas and the gas releases heat energy of $42 \mathrm{~J}$. The final internal energy of the gas is

  • A
    $20 \mathrm{~J}$
  • Correct answer
    B
    $369.6 \mathrm{~J}$
  • C
    $54 \mathrm{~J}$
  • D
    $20 \mathrm{cal}$

Solution

Initial internal energy, $\mathrm{U}_{\mathrm{i}}=80 \mathrm{cal}=80 \times 4.2 \mathrm{~J}$ Work done, $\mathrm{W}=18 \mathrm{cal}=18 \times 4.2 \mathrm{~J}$ Heat released, $Q=42 \mathrm{~J}$ Final internal energy, $\mathrm{U}_{\mathrm{f}}=$ ? using 1st law of thermodynamics $$ \begin{aligned} & \Delta Q=\Delta U+\Delta W \\ & \Delta Q=U_i-U_f+\Delta W \\ & 42=336-U_f+75.6 \\ & U_f=369.6 J \end{aligned} $$

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

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