The Joule-Thomson expansion of a gas is
(A) Isentropic
(B) Isenthalpic
(C) Isobaric
(D) Isochoric
Options:
(A) Isentropic
(B) Isenthalpic
(C) Isobaric
(D) Isochoric
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.15)**
**1. Thermodynamic Principle of Joule-Thomson Expansion**:
- A Joule-Thomson expansion involves a steady flow of gas through a porous plug or throttling valve enclosed by thermally insulated (adiabatic) boundaries ($dQ = 0$).
**2. Mathematical Derivation**:
- Let gas of mass $m$ at initial state $(P_1, V_1, T_1)$ pass through the throttling constriction to final state $(P_2, V_2, T_2)$.
- Boundary work done on the gas by the upstream pressure: $W_1 = P_1 V_1$.
- Boundary work done by the gas against downstream pressure: $W_2 = P_2 V_2$.
- Net external work done by the system:
$W = W_2 - W_1 = P_2 V_2 - P_1 V_1$
- Applying the First Law of Thermodynamics for adiabatic processes ($Q = 0$):
$\Delta U = U_2 - U_1 = Q - W = 0 - (P_2 V_2 - P_1 V_1)$
- Rearranging terms:
$U_2 + P_2 V_2 = U_1 + P_1 V_1$
- By definition of enthalpy $H = U + PV$:
$H_2 = H_1 \implies \Delta H = 0$
- Hence, the Joule-Thomson process is strictly **isenthalpic**.
**3. Official Verification**:
The verified official IIT answer is **Option (B)** (`Isenthalpic`).
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