When certain volume of gas expands against a constant external pressure of $2.40 \times 10^5 \mathrm{~Pa}$…

When certain volume of gas expands against a constant external pressure of $2.40 \times 10^5 \mathrm{~Pa}$ at $300 \mathrm{~K}$ to $2.2 \times 10^{-3} \mathrm{~m}^3$. If the work obtained is $-0.048 \mathrm{~kJ}$. What is the initial volume of the gas?
  1. $2 \times 10^{-3} \mathrm{~m}^3$
  2. $4.5 \times 10^{-2} \mathrm{~m}^3$
  3. $1.5 \times 10^{-3} \mathrm{~m}^3$
  4. $2.8 \times 10^{-2} \mathrm{~m}^3$

Solution

$\begin{aligned} & \mathrm{W}=-\mathrm{P}_{\mathrm{ext}}\left[\mathrm{V}_2-\mathrm{V}_1\right] \\ & -0.048 \times 1000 \mathrm{~J}=-2.4 \times 10^5 \mathrm{~Pa}\left[2.2 \times 10^{-3}-\mathrm{V}_1\right] \mathrm{m}^3 \\ & \frac{48}{2.8} \times 10^{-5}=2.2 \times 10^{-3}-\mathrm{V}_1 \\ & \mathrm{~V}_1=2.2 \times 10^{-3}-0.2 \times 10^{-3} \\ & \mathrm{~V}_1=2 \times 10^{-3} \mathrm{~m}^3\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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