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If ΔU and ΔW represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

1. ΔU = −ΔW, in an adiabatic process
2. ΔU = ΔW, in an isothermal process
3. ΔU = ΔW, in an isothermal process
4. ΔU = −ΔW, in an isothermal process

Correct answer: ΔU = −ΔW, in an adiabatic process

Solution

In an adiabatic process, no heat exchange occurs (Q = 0), so the first law of thermodynamics simplifies to ΔU = -ΔW. This means the change in internal energy is equal to the negative of the work done by the system.

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