Q137 / 160 · TS EAMCET 2024 (09 May Shift 2) · Physics

If $\mathrm{dQ}, \mathrm{dU}$ and dW are heat energy absorbed, change in internal energy and external work done respectively by a diamotic gas at constant pressure, then $\mathrm{dW}: \mathrm{dU}: \mathrm{dQ}$ is

  • A
    $5: 3: 2$
  • B
    $7: 5: 2$
  • C
    $4: 3: 1$
  • Correct answer
    D
    $2: 5: 7$

Solution

At constant pressure, Change in internal energy, $\mathrm{dv}=\mathrm{n}_{\mathrm{v}} \mathrm{dT}$ $\begin{aligned} & \text { Heat, } \mathrm{d} \theta=\mathrm{n} \mathrm{C}_{\mathrm{p}} \mathrm{dT} \\ & \text { Work, } \mathrm{dW}=\mathrm{PdV}=\mathrm{nRdT} \\ & \therefore \mathrm{dW}: \mathrm{dU}: \mathrm{d} \theta=\mathrm{nRdT}: \mathrm{nC}_{\mathrm{v}} \mathrm{dT}: \mathrm{nC}_{\mathrm{p}} \mathrm{dT} \\ & =\mathrm{nRdT}: \mathrm{n} \frac{5}{2} \mathrm{RdT}: \mathrm{n} \frac{7}{2} \mathrm{RdT} \\ & =2: 5: 7 \end{aligned}$

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

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