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In thermodynamics , the Joule—Thomson effect also known as the Joule—Kelvin effect or Kelvin—Joule effect describes the temperature change of a real gas or liquid as differentiated from an ideal gas when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment.

The gas-cooling throttling process is commonly exploited in refrigeration processes such as air conditioners, heat pumps, and liquefiers.

Throttling is a fundamentally irreversible process. The throttling due to the flow resistance in supply lines, heat exchangers, regenerators, and other components of thermal machines is a source of losses that limits the performance.

It followed upon earlier work by Joule on Joule expansion , in which a gas undergoes free expansion in a vacuum and the temperature is unchanged, if the gas is ideal. The adiabatic no heat exchanged expansion of a gas may be carried out in a number of ways. The change in temperature experienced by the gas during expansion depends not only on the initial and final pressure, but also on the manner in which the expansion is carried out.

This coefficient may be either positive corresponding to cooling or negative heating ; the regions where each occurs for molecular nitrogen, N 2 , are shown in the figure. Note that most conditions in the figure correspond to N 2 being a supercritical fluid , where it has some properties of a gas and some of a liquid, but can not be really described as being either.

The coefficient is negative at both very high and very low temperatures; at very high pressure it is negative at all temperatures. The maximum inversion temperature K for N 2 [10] occurs as zero pressure is approached. At temperatures below the gas-liquid coexistence curve , N 2 condenses to form a liquid and the coefficient again becomes negative. Thus, for N 2 gas below K, a Joule—Thomson expansion can be used to cool the gas until liquid N 2 forms.

There are two factors that can change the temperature of a fluid during an adiabatic expansion: a change in internal energy or the conversion between potential and kinetic internal energy.

Temperature is the measure of thermal kinetic energy energy associated with molecular motion ; so a change in temperature indicates a change in thermal kinetic energy.

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The internal energy is the sum of thermal kinetic energy and thermal potential energy. This is what happens in a Joule—Thomson expansion and can produce larger heating or cooling than observed in a free expansion. In a Joule—Thomson expansion the enthalpy remains constant. This produces a decrease in temperature and results in a positive Joule—Thomson coefficient.

If the increase in kinetic energy exceeds the increase in potential energy, there will be an increase in the temperature of the fluid and the Joule—Thomson coefficient will be negative.

## Joule Thomson Effect

For a gas, this is typically less than unity at low temperature and greater than unity at high temperature see the discussion in compressibility factor. Under such conditions, the Joule—Thomson coefficient is negative, as seen in the figure above. The physical mechanism associated with the Joule—Thomson effect is closely related to that of a shock wave , [16] although a shock wave differs in that the change in bulk kinetic energy of the gas flow is not negligible.

See the Derivation of the Joule—Thomson coefficient below for the proof of this relation.

Its pressure dependence is usually only a few percent for pressures up to bar. The temperature of this point, the Joule—Thomson inversion temperature , depends on the pressure of the gas before expansion. With that in mind, the following table explains when the Joule—Thomson effect cools or warms a real gas:.

Helium and hydrogen are two gases whose Joule—Thomson inversion temperatures at a pressure of one atmosphere are very low e. Thus, helium and hydrogen warm when expanded at constant enthalpy at typical room temperatures. In practice, the Joule—Thomson effect is achieved by allowing the gas to expand through a throttling device usually a valve which must be very well insulated to prevent any heat transfer to or from the gas.

No external work is extracted from the gas during the expansion the gas must not be expanded through a turbine , for example. The cooling produced in the Joule—Thomson expansion makes it a valuable tool in refrigeration.

A gas must be below its inversion temperature to be liquefied by the Linde cycle. For this reason, simple Linde cycle liquefiers, starting from ambient temperature, cannot be used to liquefy helium, hydrogen, or neon. However, the Joule—Thomson effect can be used to liquefy even helium, provided that the helium gas is first cooled below its inversion temperature of 40 K. In thermodynamics so-called "specific" quantities are quantities per unit mass kg and are denoted by lower-case characters.

So h , u , and v are the specific enthalpy , specific internal energy, and specific volume volume per unit mass, or reciprocal density , respectively.

In a Joule—Thomson process the specific enthalpy h remains constant. So, the total work done on the mass m of gas is. The change in internal energy minus the total work done on the amount of gas is, by the first law of thermodynamics , the total heat supplied to the amount of gas.

A very convenient way to get a quantitative understanding of the throttling process is by using diagrams. There are many types of diagrams h - T diagram, h - P diagram, etc. Commonly used are the so-called T - s diagrams.

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Figure 2 shows the T - s diagram of nitrogen as an example. As shown before, throttling keeps h constant.

At 1 bar it results in point b which has a temperature of K. So throttling from bar to 1 bar gives a cooling from room temperature to below the freezing point of water.

## Throttling Process

Throttling from bar and an initial temperature of K point c in fig. That is the purpose of this section. The first step in obtaining these results is to note that the Joule—Thomson coefficient involves the three variables T , P , and H.

A useful result is immediately obtained by applying the cyclic rule ; in terms of these three variables that rule may be written. Each of the three partial derivatives in this expression has a specific meaning.

This equation can be used to obtain Joule—Thomson coefficients from the more easily measured isothermal Joule—Thomson coefficient. It is used in the following to obtain a mathematical expression for the Joule—Thomson coefficient in terms of the volumetric properties of a fluid.

To proceed further, the starting point is the fundamental equation of thermodynamics in terms of enthalpy; this is. The appropriate relation is. Replacing these two partial derivatives yields.

## Related terms:

This provides an expression for the Joule—Thomson coefficient in terms of the commonly available properties heat capacity, molar volume, and thermal expansion coefficient. Since this is true at all temperatures for ideal gases see expansion in gases , the Joule—Thomson coefficient of an ideal gas is zero at all temperatures.

For such an ideal gas, this theoretical result implies that:. This rule was originally found by Joule experimentally for real gases and is known as Joule's second law.

## Joule–Thomson effect

More refined experiments of course found important deviations from it. From Wikipedia, the free encyclopedia. Redirected from Throttling process thermodynamics. Thermodynamic phenomenon. Perry and D. Green Perry's Chemical Engineers' Handbook. Roy Fundamentals of Classical and Statistical Thermodynamics.

## Throttling process thermodynamics pdf books

Bibcode : fcst. Edmister, B. Lee Applied Hydrocarbon Thermodynamics. Gulf Publishing. Reif Fundamentals of Statistical and Thermal Physics. Adamson The First Law of Thermodynamics". A Textbook of Physical Chemistry 1st ed.

Academic Press. Castellan Physical Chemistry 2nd ed.

Fundamentals of Engineering Thermodynamics 5th ed. Journal of Low Temperature Physics. Bibcode : JLTP.. American Journal of Physics. Bibcode : AmJPh.. Physical Chemistry 6th ed. New York: W. Freeman and Co. Chemical Thermodynamics. Cambridge University Press, Cambridge, U. Gases, liquids and solids , p. Rosenberg Chemical Thermodynamics , p.

Benjamin, Meno Park, California. Physical Review Letters. Bibcode : PhRvL.