Based on the first law of thermodynamics, which one of the following is correct?

Question: Based on the first law of thermodynamics, which one of the following is correct?

A   For an isothermal process, q= +w

B   For an isochoric process, ΔU=−q

C   For an adiabatic process, ΔU=−w

D   For a cyclic process, q=−w

Answer:     For a cyclic process, q=−w

 Mathematical Equation Explanation ∆U = q – w ∆U = 0 0 = q – w q = -w ·        The first law states that ∆U of a system is equal to the q- w. Where: ·        ∆U represents the change in internal energy of the system during the cyclic process. ·        q represents the heat added to the system during the cyclic process. ·        W represents the work done by the system during the cyclic process. ·        A cyclic process is one where a system returns to its initial state after a series of changes, which means ∆U = 0 because the internal energy change cancels out. ·        Rearranging the equation, we find that in a cyclic process, the heat added (q) is equal in magnitude but opposite in sign to the work done (w) by the system. ·        Summary: For a cyclic process, q and w have equal magnitudes, but their signs are opposite. This relationship illustrates the conservation of energy, where the heat added to the system is fully accounted for by the work done by the system and vice versa.