Question

In a thermodynamic system, $\Delta U$ represents the increase in internal energy and $dW$ the work done by the system. Then correct statement is

• A. $\Delta U=dW$ is an isothermal process
• B. $\Delta U=-dW$ is an adiabatic process
• C. $\Delta U=-dW$ is an isothermal process
• D. $\Delta U=dW$ is an adiabatic process

Hint:

Physics Tip: Adiabatic process means no heat exchange: $Q=0$.

Answer 1

The Correct Option is B

Step 1: Apply first law of thermodynamics. The first law is: $$ dQ=\Delta U+dW $$ where
• $dQ$ = heat supplied to system
• $\Delta U$ = change in internal energy
• $dW$ = work done by system

Step 2: Understand adiabatic process. In an adiabatic process, no heat enters or leaves system. $$ dQ=0 $$

Step 3: Substitute in first law. $$ 0=\Delta U+dW $$ Therefore, $$ \Delta U=-dW $$

Step 4: Interpret meaning. If system does work, internal energy decreases. If work is done on system, internal energy increases.

Step 5: Conclusion. This relation belongs to adiabatic process. $$ \therefore \text{Correct option is (B).} $$