A gas absorbs \(200 \mathrm{~J}\) heat and expands by \(500 \mathrm{~cm}^3\) against a constant external pressure \(2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}\). What is the change in internal energy?

\(\begin{aligned} & \Delta V=500 \mathrm{~cm}^3=0.5 \mathrm{dm}^3 \\ & \mathrm{P}_{\mathrm{ext}}=2 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}=2 \text { bar } \\ & \text { (since, } 1 \times 10^5 \mathrm{~N} \mathrm{~m}^{-2}=1 \text { bar) } \\ & \mathrm{W}=-\mathrm{P}_{\mathrm{ext}} \times \Delta \mathrm{V} \\ & =-2 \times(0.5) \\ & =-1 \mathrm{dm}^3 \text { bar } \\ & \therefore \quad \mathrm{W}=-100 \mathrm{~J} \quad\left(\text { since, } 1 \mathrm{dm}^3 \mathrm{bar}=100 \mathrm{~J}\right) \\ & \text { According to first law of thermodynamics, } \\ & \Delta U=Q+W=200 \mathrm{~J}-100 \mathrm{~J}=+100 \mathrm{~J} \\ & \end{aligned}\)