The Joule Thomson effect refers to a thermodynamic process that occurs when the expansion of fluid takes place from high pressure to low pressure at constant enthalpy. Furthermore, the approximation of such process takes place in the real world by facilitating an expansion of fluid from high pressure to low pressure across a valve. Also, the Joule-Thomson effect and inversion temperature is dependent on the gasâ€™s pressure before expansion

**Introduction to Joule Thomson EffectÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â **

The Joule-Thomson effect, also known as the Joule-Kelvin effect, refers to the change which takes place in fluidâ€™s temperature as it flows from a region of higher pressure to lower pressure. One can describe the Joule-Thomson effect by means of the Joule-Thomson coefficient. Also, the Joule-Thomson coefficient is the partial pressure derivative with respect to temperature at constant enthalpy.

The Joule-Thomson coefficient would vary as a function of temperature and pressure. Furthermore, the Joule-Thomson coefficient would vary from one fluid to another. Also, the inversion curve refers to the curve that is described by the Joule-Thomson coefficient equalling zero as a function of temperature and pressure.

### How do we Measure the Joule Thomson Effect?

TheÂ adiabaticÂ (no heat exchanged) expansion of a gas can take place in a number of ways, as part of the Joule-Thomson effect experiment. The change in temperature which a gas experiences during expansion is dependent not only on the initial pressure and final pressure but also on the manner the expansion takes place.

If the expansion process isÂ reversible, such that the gas would be always inÂ thermodynamic equilibrium, the expansion isÂ isentropic. Here, the temperature of the gas decreases and it does positiveÂ workÂ during the expansion.

The gas does no work in free expansion and no absorption of heat takes place. As such, there is a conservation of internal energy.Â Here, the ideal gasâ€™s temperatureÂ would remain constant but the real gasâ€™s temperature would decrease, except at extremely high temperature.

The Jouleâ€“Thomson expansion refers to a method of expansion in which a gas or liquid at pressureÂ *P*_{1}, without a considerable change in kinetic energy, flows into a region of lower pressureÂ *P*_{2}. The expansion is certainly inherently irreversible.

During such an expansion,Â there would be no change in enthalpy. Furthermore, the determination of whether the internal energy increases or decreases takes place by whether work is done by the liquid or on the fluid. This means that it is determined by the initial and final states of the fluidâ€™s properties.

The Jouleâ€“Thomson coefficient makes possible the quantification of the temperature change during a Jouleâ€“Thomson expansion display. Furthermore, this coefficient may be either positive or negative. Moreover, being positive corresponds to cooling while being negative corresponds to heating.

The coefficient turns out to be negative at extremely high and extremely low temperatures. Furthermore, it is negative at very high pressure at all temperatures. Also, the maximumÂ inversion temperatureÂ (621 K for N_{2}) takes place as the zero pressure approaches.

At temperatures that are below the gas-liquidÂ coexistence curve, the condensation of N_{2}Â takes place to form a liquid. Moreover, the coefficient would once again become negative. Thus, for N_{2}Â gas below 621 K, a Jouleâ€“Thomson expansion can be used to cool the gas until the formation of liquid N_{2}Â takes place.

**Formula of Joule Thomson Effect**

The Joule Thomson effect formula is below

Î¼JT = (âˆ‚T/âˆ‚P)H

For a gas temperature that is above the inversion temperature, the Î¼JT would be negative. The âˆ‚P shall be always negative in this case, which means that the âˆ‚ must be positive. Consequently, the warming of the gas will take place.

**Derivation of the Formula of Joule Thomson Effect**

First is the throttling process. Here, the enthalpy must be constant partially because only local conditions must be considered.

Consider the pushing of the fluid taking place by a piston. This exerts a pressureÂ Pi, while a need for a second piston arises to enable the fluid to pass through. The second piston will have the pressureÂ Pf, to facilitate backward movement.

ViÂ is the initial volume whileÂ VfÂ is the final volume.

Assume that no heat flow takes place, so energy change is

U_{f} â€“ U_{i} = Q + W, which in turn is = 0 +W_{left }+ W_{right}

Take W_{left –}Â to be positive andÂ W_{right }as negative. Therefore, the change in energy is

U_{f} â€“ U_{i} = P_{i}V_{i} â€“ P_{f}V_{f}

Rearranging this will provide

Uf + P_{f}V_{f}Â = U_{i} + P_{i}V_{i}

orÂ H_{f} = H_{i} so enthalpy is constant during the throttling process, soÂ âˆ‚H = 0

It is certainly difficult to think what is the physical representation of the Jouleâ€“Thomson coefficient,Â Î¼JT. Also, modern determinations ofÂ Î¼JT avoid the original method that was used by Joule and Thomson. Rather, measurements take place with a different, closely related quantity.

There are three variables T,Â P, andÂ H that the Jouleâ€“Thomson coefficient involves. Moreover, one can obtain a useful result immediately by applying theÂ cyclic rule. Furthermore, one may write the rule in terms of these three variables as

(âˆ‚T/âˆ‚P)_{H}(âˆ‚H/âˆ‚T)_{P}(âˆ‚P/âˆ‚H)_{T} = âˆ’1

Each of the three partial derivatives in this expression would carry a specific meaning. The first isÂ Î¼JT, while the second is the constant pressureÂ heat capacity,Â Cp

Cp = (âˆ‚H/âˆ‚T)P

and the third partial derivative is the inverse of theÂ isothermal Jouleâ€“Thomson coefficient,Â Î¼T

Î¼T = (âˆ‚H/âˆ‚P)T

**FAQs on Joule Thomson Effect**

**Question 1: Briefly explain the Joule Thomson effect?**

**Answer 1:** The Joule Thomson effect is simply a thermodynamic process. Furthermore, this process happens when the expansion of fluid takes place from high to low pressure at constant enthalpy.

**Question 2: What are the factors on which the change in temperature is experienced by gas during expansion?**

**Answer 2:** The factors on which the change in temperature which a gas experiences during expansion are initial pressure, final pressure, and the manner in which the expansion is carried out.

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