A gas is compressed from a volume of $2\,m^3$ to a volume of $1\, m^3$ at a constant pressure of $100\, N/m^2$. Then it is heated at constant volume by supplying $150\, J$ of energy. As a result, the internal energy of the gas
JEE MAIN 2014, Medium
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As we know, $\Delta Q=\Delta u+\Delta w$
(Ist law of thermodynamics) $\Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{u}+\mathrm{P} \Delta \mathrm{v}$
or $150=\Delta u+100(1-2)$
$=\Delta u-100$
$\therefore \Delta u=150+100=250 \mathrm{J}$
Thus the internal energy of the gas increases by $250 \mathrm{J}$
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