A gas absorbs $150 \mathrm{~J}$ heat and expands by $300 \mathrm{~cm}^3$ against a constant external…

A gas absorbs $150 \mathrm{~J}$ heat and expands by $300 \mathrm{~cm}^3$ against a constant external pressure $2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}$, What is $\Delta \mathrm{U}$ of the system?
  1. $210 \mathrm{~J}$
  2. $90 \mathrm{~J}$
  3. $450 \mathrm{~J}$
  4. $-300 \mathrm{~J}$

Solution

$\begin{array}{rl} 300 \mathrm{~cm}^3=300 \times 10^{-6} \mathrm{~m}^3 & \mathrm{~W} \\ & =-\mathrm{P}_{\text {ext }} \Delta \mathrm{V} \\ & =-2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2} \times\left(300 \times 10^{-6} \mathrm{~m}^3\right) \\ & =-60 \mathrm{~N} \mathrm{~m} \\ & =-60 \mathrm{~J} \\ \therefore \quad \mathrm{W} & =-60 \mathrm{~J} \end{array}$ Now, $\begin{aligned} \therefore \quad \Delta \mathrm{U} & =\mathrm{q}+\mathrm{P}_{\text {ext }} \Delta \mathrm{V} \\ & =150 \mathrm{~J}+(-60 \mathrm{~J}) \\ & =90 \mathrm{~J} \end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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