A gas is allowed to expand in an insulated container against a constant external pressure of 2.5 bar from $4…

A gas is allowed to expand in an insulated container against a constant external pressure of 2.5 bar from $4.5 \mathrm{dm}^3$ to $7 \times 10^{-3} \mathrm{~m}^3$. What is the change in internal energy of the gas?
  1. $-625 \mathrm{~J}$
  2. $-312.5 \mathrm{~J}$
  3. $-112.3 \mathrm{~J}$
  4. $-3.25 \mathrm{~J}$

Solution

Container is insulated $\therefore \delta Q=0$ We know $\Delta \mathrm{E}=\delta \mathrm{Q}+\delta \mathrm{W}$ $\begin{aligned} & =0+\left[-\mathrm{P}\left(\mathrm{V}_2-\mathrm{V}_1\right)\right] \\ & =-2.5(7-4.5) \\ & =-2.5(2.5) \times 100 \\ & =-625 \mathrm{~J}\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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