 # Joule-Thomson Effect

What is Joule Thomson Effect in Thermodynamics?

Joule Thomson effect illustrates the change in temperature of a fluid when it is forced to flow through an insulated valve from a high-pressure region towards a region with low pressure. Joule Thomson effect is often termed the Joule Kelvin or Kelvin Joule effect. According to their theory, change in pressure in the valve can cause changes in the temperature of the fluid.

Joule Thomson Experiment

Refer to the image shown above that helps understand the effect of Joule Thomson law quickly. To illustrate this, a gas packet is placed opposite to the flow of direction in a Joule Thomson valve. As a result, it faces restriction, and the upstream gas will need to perform work to help it move. This work done is equivalent to the multiplication of upstream pressure and volume of a packet.

W1 = VPacket1 x P1

Further, the fluid packet has to perform certain work to make a place for itself by displacing some amount of downstream gas. This work done can be expressed as

W2 = VPacket2 x P2

However, this work performed upstream and work performed downstream is not equal because of various effects of compressibility. This internal energy of fluid follows the 1st law of thermodynamics. And the adiabatic process does not allow this system to lose any heat or work.

From the above theories, we can conclude that

U2 – U1 = W1 – W2

For cases where the fluid pressure is lowered, there is a rise in aggregate distance between molecules. As a result, the increased attractive forces also cause an increase in potential energy.

Further, it is seen that real gases need to work more downstream to make a place for the packets than they need to work upstream.

Therefore, the following equation can be written

P1 x V1 < P2 x V2

It also illustrates a decrease in potential energy as the fluid goes through restriction. Most real gases show a reduction in temperature with a decrease in pressure. However, that does not hold true for every condition or gas. To conclude, the temperature of this fluid varies with varying potential energy, given the enthalpy of the gas remains unchanged.

Joule Thomson Coefficient

It can be defined as the change in temperature of the fluid with the varying pressure in order to keep its enthalpy constant. It can be expressed as follows

μJT = (∂T / ∂P) H

Joule Thomson Expansion

The coefficient is to be derived using the law of thermodynamics and will be written as,

μ = (∂T / ∂P)H  (∂T / ∂P)T (∂P / ∂T)H (∂T / ∂H)P

= -1 (∂H / ∂P)T

= − (∂H / ∂T)P (∂T/ ∂P)H  (∂H / ∂P)T

= – CP μ

Further,

(∂H / ∂P)T = [v~ − T (∂v / ∂T)P

μ= RT2 PCP (∂Z / ∂T) P μ

= (∂T / ∂P)H

= 1/CP [T. (∂v / ∂T)P−v]

=−1/ CP (∂H / ∂P)T

= RT2 / PCP (∂Z / ∂T)P

Mentioned above is the expansion, which will help you calculate the Joule Thomson coefficient for real gas step by step. Learn the steps carefully to understand the derivation procedure.

Inversion temperature is the fluid’s temperature at which there is no change in pressure even with decrease in temperature.

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