In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas…
In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases \(30 \mathrm{~J}\) of heat and \(10 \mathrm{~J}\) of work was done on the gas. If the initial internal energy of the gas was \(10 \mathrm{~J}\), then the final internal energy will be
\(2 \mathrm{~J}\)
\(-18 \mathrm{~J}\)
\(10 \mathrm{~J}\)
\(58 \mathrm{~J}\)
Solution
Given, heat, \(Q=-30 \mathrm{~J}\)
Work done on the gas, \(W=-10 \mathrm{~J}\)
Initial internal energy, \(U_i=-10 \mathrm{~J}\)
Final internal energy, \(U_f=\) ?
According to first law of thermodynamics,
$\begin{aligned}
& Q=W+\Delta U \\
\Rightarrow & -30=-10+U_{i}-U_{f} \\
\Rightarrow & -30=-10-10-U_{f} \\
\Rightarrow & 30=10+10+U_{f} \\
\Rightarrow & 30-20=U_{f} \\
\Rightarrow & U_{f}=10 \text{~J}
\end{aligned}$