One mole of a gas occupying 3 L volume is expanded against a constant external pressure of 1 bar to a volume…

One mole of a gas occupying 3 L volume is expanded against a constant external pressure of 1 bar to a volume of 15 L. Calculate work done by the system
  1. $1.200 \times 10^3 \mathrm{~J}$
  2. $-2.43 \times 10^3 \mathrm{~J}$
  3. $-1.200 \times 10^3 \mathrm{~J}$
  4. $2.43 \times 10^3 \mathrm{~J}$

Solution

$\begin{aligned} \mathrm{V}_1 & =3 \mathrm{~L}=3 \mathrm{dm}^3 \\ \mathrm{~V}_2 & =15 \mathrm{~L}=15 \mathrm{dm}^3 \\ \mathrm{~W} & =-\mathrm{P}_{\mathrm{ext}} \Delta \mathrm{V} \\ & =-\mathrm{P}_{\mathrm{ext}}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\ & =-1 \mathrm{bar}\left(15 \mathrm{dm}^3-3 \mathrm{dm}^3\right) \\ & =-12 \mathrm{dm}^3 \mathrm{bar} \\ & =-12 \mathrm{dm}^3 \text { bar } \times 100 \frac{\mathrm{~J}}{\mathrm{dm}^3 \mathrm{bar}} \\ & =-1.200 \times 10^3 \mathrm{~J}\end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 2)

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