The Joule Thomson Effect & Zeroth Law of Thermodynamics | Physical Chemistry PDF Download

The Joule Thomson Effect

The phenomenon of change of temperature produced when a gas is made to expand adiabatically from a region of high pressure to a region of externally low pressure is known as the Joule-Thomson Effect.
The ratio of change in temperature w.r.t. change in pressure at constant enthalpy is known as JouleThomson coefficient.  This experiment is known as Joule Thomson experiment.

Suppose a certain amount of gas is passed through the porous plug.  We than have
Change in volume on the left hand side = – V₁
Work involved on the left hand side = P₁V₁
Change in volume on right hand side = V₂
Work involved on the right hand side = – P₂V₂
Net work involved in the system = – P₂V₂ + P₁V₁ 
Because the process is adiabat ic, dq = 0 then from first law
We have, dq = dU – ω = 0
dU = ω
or U₂ – U₁ = – P₂V₂ + P₁V₁
U₂ + P₂V₂ = U₁ + P₁V₁
or
H₂ = H₁
i.e., adiabatic process is isoenthalpic in Joule-Thomson experiment.
Joule Thomson coefficient is represented by  mJ.T and is equal to

We now that,
H = H(P,T)

                  

⇒
⇒

We know that  

 then we have,

 

i.e.   

Inversion temperature: The temperature at which the Joules-Thomson coefficient changes sign is known as the inversion temperature. Another words, inversion temperature is the temperature at which real gas behave ideally.
We know that μ_{J .T.} = 0 for ideal gas

 

⇒ 
⇒

Where T_i is known as inversion temperature.

Zeroth law of thermodynamics: “If body A is in equilibrium with body B is also in equilibrium with body C, then bodies A and B are in equilibrium with each other.”