• # question_answer A gas expands isothermally against a constant external pressure of I atmosphere from a volume of $10\text{ }d{{m}^{3}}$to a volume of $20\text{ }d{{m}^{3}}.$In this process it absorbs 800 J of thermal energy from its surroundings. The $\Delta U$for the process in Joules is A)  -113 J                        B)  +113 J          C)                   -213 J             D)       +313 J

We know that$W=-\int\limits_{{{V}_{1}}}^{{{V}_{2}}}{PdV}$ Here, P = constant. So, $W=-P({{V}_{2}}-{{V}_{1}})$ $W=-(1)(20-10)=-10\,d{{m}^{3}}\,\text{atm}$ $=-10\,d{{m}^{3}}\times \frac{8.314\,J{{K}^{-1}}\,mo{{l}^{-1}}}{0.08206\,d{{m}^{3}}\,mo{{l}^{-1}}}$ $W=-1013\,J.$ Now using the first law of thermodynamics, $\Delta U=Q+W=80\,J+(-1013)=-213\,J.$ Hence, the correct option is (c).