Thermodynamic Process Matching

This question requires matching thermodynamic processes (LIST-I) with their characteristic mathematical conditions (LIST-II).

Matching Process Definitions

• A. Isothermal Process: This process occurs at a constant temperature ($\Delta T = 0$). For an ideal gas, the internal energy ($u$) depends only on temperature. Therefore, in an isothermal process, the change in internal energy is zero ($\Delta u = 0$), meaning $\text{du} = 0$. This matches with Roman numeral II.
• B. Isochoric Process: This process occurs at a constant volume ($\Delta V = 0$). Work done ($w$) is defined as $w = \int P \text{dV}$. Since the volume change is zero, the work done is zero ($\Delta w = 0$), meaning $\text{dw} = 0$. This matches with Roman numeral III.
• C. Adiabatic Reversible Process: An adiabatic process is one where there is no heat exchange with the surroundings ($\text{dq} = 0$). A reversible adiabatic process is also isentropic, meaning the entropy ($s$) remains constant ($\Delta s = 0$), so $\text{ds} = 0$. This matches with Roman numeral I.
• D. Adiabatic Process: The defining characteristic of any adiabatic process (reversible or irreversible) is that no heat is transferred between the system and its surroundings. Therefore, the heat transfer ($q$) is zero ($\Delta q = 0$), meaning $\text{dq} = 0$. This matches with Roman numeral IV.

Correct Matches Summary

Based on the definitions:

• A matches with II ($\text{du} = 0$)
• B matches with III ($\text{dw} = 0$)
• C matches with I ($\text{ds} = 0$)
• D matches with IV ($\text{dq} = 0$)

The correct combination is A-II, B-III, C-I, D-IV.