In a thermodynamic system ' $\Delta \mathrm{U}$ ' represents the increase in internal energy and 'W' the…
In a thermodynamic system ' $\Delta \mathrm{U}$ ' represents the increase in internal energy and 'W' the work done by the system. Which of the following statement is true?
$\Delta \mathrm{U}=-\mathrm{W}$ in an adiabatic process.
$\Delta \mathrm{U}=\mathrm{W}$ in an isothermal process.
$\Delta \mathrm{U}=-\mathrm{W}$ in an isothermal process.
$\Delta U=W$ in an adiabatic process.
Solution
For an isothermal process, $\Delta \mathrm{U}=0$. According to first law of thermodynamics, $\Delta \mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}$
For an adiabatic process,
$\begin{array}{rlrl}
& & \Delta \mathrm{Q} & =0 \\
\therefore \quad & \Delta \mathrm{U} & =-\mathrm{W}
\end{array}$