Two moles of an ideal gas is expanded isothermally from a volume of $300 \mathrm{~cm}^3$ to 2.5…

Two moles of an ideal gas is expanded isothermally from a volume of $300 \mathrm{~cm}^3$ to 2.5 $\mathrm{dm}^3$ at 298 K against a constant pressure at 1.9 bar. Calculate the work done in joules.
  1. -418 J .
  2. $-565 \mathrm{~J}$
  3. -918 J
  4. $-950 \mathrm{~J}$

Solution

$\begin{aligned} & \mathrm{V}_1=300 \mathrm{~cm}^3=0.3 \mathrm{dm}^3,\left(\because 1 \mathrm{dm}^3=1.000 \mathrm{~cm}^3\right) \\ & \mathrm{V}_2=2.5 \mathrm{dm}^3\end{aligned}$ $\begin{aligned} \mathrm{P}_{\mathrm{ext}} & =1.9 \mathrm{bar} \\ \mathrm{W} & =-\mathrm{P}_{\mathrm{ext}}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\ & =-1.9(2.5-0.3) \\ & =-4.18 \mathrm{dm}^3 \mathrm{bar} \times 100 \frac{\mathrm{~J}}{\mathrm{dm}^3 \mathrm{bar}} \\ \therefore \quad \mathrm{W} & =-418 \mathrm{~J}\end{aligned}$

Asked in: MHT CET 2024 (09 May Shift 1)

Practice more Chemical Thermodynamics questions on Aicharya