One mole of an ideal gas undergoes a reversible Carnot cycle consisting of four steps: isothermal expansion (from V₁ to V₂ at T_ high ), adiabatic expansion (to V₃ at T_ low ), isothermal compression (to V₄ at T_ low ), and adiabatic compression (back to V₁ at T_ high ). Match the thermodynamic quantities in List-I with their expressions in List-II. List-I List-II (A) Work done in adiabatic expansion (I) Zero (B) Hea

Step-by-step solution

According to the IUPAC sign convention, the first law of thermodynamics is U = q + w . For the adiabatic expansion from T_ high to T_ low : q = 0 , so w = U = C_v(T_ low - T_ high ) . Thus, (A) matches (II). For the isothermal compression from V₃ to V₄ at T_ low : The change in internal energy U = 0 . Work done w = -RT_ low ( V₄ V₃ ) . Heat exchanged q = U - w = RT_ low ( V₄ V₃ ) . Thus, (B) matches (IV). For any complete cyclic process, internal energy is a state function, so the net change U_ cycle = 0 . Thus, (C