In a thermodynamic process if ' $\Delta \mathrm{W}$ ' and ' $\Delta \mathrm{U}$ ' are the work done and…
In a thermodynamic process if ' $\Delta \mathrm{W}$ ' and ' $\Delta \mathrm{U}$ ' are the work done and change in the internal energy of a system respectively, then
$\Delta \mathrm{U}=\Delta \mathrm{W}$ in adiabatic process
$\Delta \mathrm{U}=\Delta \mathrm{W}$ in isothermal process
$\Delta \mathrm{U}=-\Delta \mathrm{W}$ in isothermal process
$\Delta \mathrm{U}=-\Delta \mathrm{W}$ in adiabatic process
Solution
Using Ist law of thermodynamics
$\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W}$
for adiabatic process, $\Delta Q=0$
$\therefore \Delta \mathrm{U}=-\Delta \mathrm{W}$