In a thermodynamic system, $\Delta U$ represents the increases in its internal energy and $\mathrm{dW}$ is…
In a thermodynamic system, $\Delta U$ represents the increases in its internal energy and $\mathrm{dW}$ is the work done by the system then correct statement out of the following is
$\Delta \mathrm{U}=\mathrm{dW}$ is an isothermal process
$\Delta \mathrm{U}=-\mathrm{dW}$ is an adiabatic process
$\Delta \mathrm{U}=-\mathrm{dW}$ is an isothermal process
$\Delta \mathrm{U}=\mathrm{dW}$ is an adiabatic process
Solution
For an isothermal process, $\Delta \mathrm{U}=0$.
According to first law of thermodynamics, $\Delta \mathrm{Q}=\Delta \mathrm{U}+\mathrm{dW}$
For an adiabatic process,
$\Delta Q=0$
$\therefore \quad \Delta \mathrm{U}=-\mathrm{dW}$
$\therefore \quad$ It is an adiabatic process.