Thermodynamics Matching: LIST-I & LIST-II

This question requires matching thermodynamic properties in LIST-I with their corresponding definitions or mathematical expressions from LIST-II.

Entropy Definition

Entropy ($S$) is a measure of disorder. The change in entropy ($dS$) for a reversible process is defined as the heat transferred ($\partial q$) divided by the absolute temperature ($T$). $dS = \frac{\partial q_{rev}}{T}$ Therefore, Entropy (A) corresponds to III ($\frac{\partial q}{T}$).

Cp Definition

The specific heat capacity at constant pressure ($C_P$) is defined as how much energy is needed to raise the temperature of one mole (or unit mass) of a substance by one degree Celsius (or Kelvin) while keeping the pressure constant. Mathematically, it's the partial derivative of enthalpy ($H$) with respect to temperature ($T$) at constant pressure ($P$). $C_P = \left( \frac{\partial H}{\partial T} \right)_P$ Therefore, $C_P$ (B) corresponds to IV ($\left( \frac{\partial H}{\partial T} \right)_P$).

Cv Definition

The specific heat capacity at constant volume ($C_V$) is defined similarly to $C_P$, but at constant volume. It represents the change in internal energy ($U$) with respect to temperature ($T$) at constant volume ($V$). $C_V = \left( \frac{\partial U}{\partial T} \right)_V$ Therefore, $C_V$ (C) corresponds to I ($\left( \frac{\partial U}{\partial T} \right)_V$).

Joule-Thomson Co-efficient Definition

The Joule-Thomson Expansion Co-efficient ($\mu_{JT}$) measures the change in temperature ($T$) of a gas per unit change in pressure ($P$) during a process where the enthalpy ($H$) remains constant (isenthalpic process). $\mu_{JT} = \left( \frac{\partial T}{\partial P} \right)_H$ Therefore, Joule-Thomson Expansion Co-efficient (D) corresponds to II ($\left( \frac{\partial T}{\partial P} \right)_H$).

Final Match

Based on the definitions, the correct pairings are:

A - III, B - IV, C - I, D - II