Question

Obtain the formula for the Joule–Thompson effect 

ΔT = [T(∂V/∂T)_P − V]ΔP/C_P

Answer 1

In the Joule–Thompson effect heat does not enter the expanding gas, that is ΔQ = 0. The net work done by the external forces on a unit mass of the gas is (P₁V₁ − P₂V₂), where P₁ and P₂ refer to higher and lower pressure across the plug respectively. 

ΔW = P₁V₁ − P₂V₂ 

If the internal energy of unit mass is U₁ and U₂ before and after the gas passes through the plug 

ΔU = U₁ − U₂ 

By the first law of Thermodynamics 

ΔQ = 0 = ΔW + ΔU 

or U₂ − U₁ = P₁V₁ − P₂V₂ 

or Δ(U + PV) = 0 

or ΔH = 0