@wikipedia
The rate of change of temperature | LaTeX Math Inline |
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| body | --uriencoded-- %7B\displaystyle T%7D |
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with respect to pressure | LaTeX Math Inline |
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| body | --uriencoded--%7B\displaystyle P%7D |
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in a throttling process:
| LaTeX Math Block |
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\epsilon_{JT} = \left( \frac{\partial T}{\partial P} \right)_{H} = \frac{\alpha_V \cdot T - 1}{c_{vp}} |
where
For the Ideal Gas:
| LaTeX Math Inline |
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| body | --uriencoded--\alpha_V = \frac%7B1%7D%7BT%7D |
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and
Joule–Thomson coefficient is strictly zero:
| LaTeX Unit |
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| body | --uriencoded--\epsilon_%7BJT%7D = 0 |
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.
In case of general Fluid:
| LaTeX Math Inline |
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| body | \alpha_V = \alpha_V (T) |
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and the temperature
| LaTeX Math Inline |
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| body | --uriencoded--T_%7B\rm inv%7D |
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where
| LaTeX Math Inline |
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| body | --uriencoded--T_%7B\rm inv%7D \cdot \alpha_V(T_%7B\rm inv%7D) = 1 |
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is called
Inversion Temperature.
The Fluid above Inversion Temperature
| LaTeX Math Inline |
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| body | --uriencoded--T > T_%7B\rm inv%7D |
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has negative
Joule–Thomson coefficient | LaTeX Math Inline |
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| body | --uriencoded--\epsilon_%7BJT%7D <0 |
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and hence will be cooling under expansion ().
The Fluid below Inversion Temperature
| LaTeX Math Inline |
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| body | --uriencoded--T < T_%7B\rm inv%7D |
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has positive
Joule–Thomson coefficient | LaTeX Math Inline |
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| body | --uriencoded--\epsilon_%7BJT%7D >0 |
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and hence will be warming under expansion ().
See also
Physics / Thermodynamics / Thermodynamic process / Throttling Temperature Effect
