Question

In a thermodynamic pross if '$\Delta W$' and '$\Delta U$' are the work done and change in the internal energy of a system respectively, then

• A. $\Delta U = \Delta W$ in adiabatic process
• B. $\Delta U = \Delta W$ in isothermal process
• C. $\Delta U = -\Delta W$ in isothermal process
• D. $\Delta U = -\Delta W$ in adiabatic process

Hint:

Thermodynamic Processes Recap:

• Adiabatic: $\Delta Q = 0 \Rightarrow \Delta U = -\Delta W$
• Isothermal: $\Delta T = 0 \Rightarrow \Delta U = 0$, so $\Delta Q = \Delta W$
• Isochoric: $\Delta V = 0 \Rightarrow \Delta W = 0$, so $\Delta U = \Delta Q$

Answer 1

The Correct Option is D

According to the first law of thermodynamics: \[ \Delta U = \Delta Q - \Delta W \] In an adiabatic process, there is no heat exchange, so $\Delta Q = 0$. Hence: \[ \Delta U = -\Delta W \] This means that the change in internal energy is equal to the negative of the work done by the system. If the system does positive work, internal energy decreases. Hence, option (4) is correct. The other options either confuse adiabatic and isothermal conditions or misapply the signs in the first law.