Joule-Kelvin coefficient is given by [where T = absolute temperature, P = Pressure, s = Specific entropy, h = Specific enthalpy]

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  1. \(\left(\frac{\partial T}{\partial s}\right)_h\)
  2. \(\left(\frac{\partial s}{\partial T}\right)_h\)
  3. \(\left(\frac{\partial T}{\partial P}\right)_h\)
  4. \(\left(\frac{\partial T}{\partial s}\right)\)

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Option 3 : \(\left(\frac{\partial T}{\partial P}\right)_h\)
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Explanation:

Joule – Thomson coefficient:- When the gas in steady flow passes through a constriction, e.g. in an orifice or valve, it normally experiences a change in temperature. From the first law of thermodynamics, such a process is isenthalpic and one can usefully define a Joule – Thomson coefficient as

\(\mu = {\left( {\frac{{\partial T}}{{\partial P}}} \right)_H}\)

As a measure of the change in temperature which results from a drop in pressure across the construction.

  • For an ideal gas, μ = 0, because ideal gases neither warm not cool upon being expanded at constant enthalpy.
  • If μ is +ve, then the temperature will fall during throttling.
  • If μ is -ve, then the temperature will rise during throttling.

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