Find the constant external pressure required to expand a gas from 2.5 L to 4.5 L if amount of work done is…

Find the constant external pressure required to expand a gas from 2.5 L to 4.5 L if amount of work done is 500 J at 298 K ?
  1. 1 bar
  2. 2.0 bar
  3. 1.5 bar
  4. 2.5 bar

Solution

$\begin{aligned} \mathrm{V}_1 & =2.5 \mathrm{~L}, \mathrm{~V}_2=4.5 \mathrm{~L}, \\ \mathrm{~W} & =-500 \mathrm{~J}=-5 \mathrm{dm}^3 \text { bar }\left(\because 100 \mathrm{~J}=1 \mathrm{dm}^3 \text { bar }\right) \\ \mathrm{W} & =-\mathrm{P}_{\mathrm{ext}} \Delta \mathrm{V} \\ \therefore \quad \mathrm{P}_{\mathrm{ext}} & =-\frac{\mathrm{W}}{\Delta \mathrm{V}}=-\frac{\mathrm{W}}{\left(\mathrm{V}_2-\mathrm{V}_1\right)} \\ & =\frac{-\left(-5 \mathrm{dm}^3 \mathrm{bar}\right)}{(4.5-2.5) \mathrm{dm}^3}=2.5 \text { bar }\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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