A gas is compressed from a volume of \(2 \mathrm{~m}^3\) to a volume of \(1 \mathrm{~m}^3\) at a constant…
A gas is compressed from a volume of \(2 \mathrm{~m}^3\) to a volume of \(1 \mathrm{~m}^3\) at a constant pressure of \(100 \mathrm{Nm}^{-2}\). Then it is heated at constant volume by supplying \(150 \mathrm{~J}\) of energy. As a result, the internal energy of the gas
increase by \(250 \mathrm{~J}\)
decrease by \(250 \mathrm{~J}\)
decrease by \(50 \mathrm{~J}\)
increase by \(50 \mathrm{~J}\)
Solution
Since, gas is compressed from \(2 \mathrm{~m}^3\) to \(\mathrm{lm}^3\). Hence, work done on the gas is negative.
\(W=-p \Delta V=-100(2-1)=-100 \mathrm{~J}\)
Since, heat supplied, \(Q=150 \mathrm{~J}\)
Hence, according to first law of thermodynamics,
\(\begin{aligned}
Q & =W+\Delta U \\
\Rightarrow \quad 150 & =-100+\Delta U \\
\Delta U & =150+100=250 \mathrm{~J}
\end{aligned}\)