Joule Thomson Effect: Adiabatic Free Expansion & Derivation

In summary, the Joule-Thompson coefficient is a measure of the efficiency of a process that is neither isothermal, adiabatic, cyclic, or reversible. The Joule-Thompson experiment was used to derive the Rankine equation of state, which in turn provided a temperature scale that is independent of the thermometer chosen.
  • #1
akhyansh
1
0
Is the equation
JT = (1/Cp)(2a/RT - b)
valid for adiabatic free expansion of real gases only? How was this equation derived?
 
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  • #2
The expression you provide appears to be dependent on a specific equation of state (you use Van der Waals, if I may hazard a guess),but the Joule-Thompson experiment is much more general that that.

The Joule-Thompson coefficient is defined as ∂T/∂P at constant enthalpy,and represents a process that is neither isothermal, adiabatic, cyclic, or reversible (throttling of gases). The general expression is

[tex] (\frac{\partial T}{\partial P})_{H} = \frac{-V}{C_{P}}(1-T\alpha_{T})[/tex]

Historically, the Joule-Thompson experiment led to the development of an absolute temperature scale.
 
  • #3
Look also here.

Historically, the Joule-Thompson experiment led to the development of an absolute temperature scale.

Could you explain that a little more? Because I thought the absolute temperature scale was a consequence of Carnot theorems.
 
  • #4
Carcul said:
Look also here.

Could you explain that a little more? Because I thought the absolute temperature scale was a consequence of Carnot theorems.

They are related- the experiment was carried out to measure "Carnot's function", which is essentially the efficiency of a Carnot cycle engine (Carnot-Clapeyron theorem).

The details are presented in Truesdell's "The Tragicomical History of Thermodynamics (1822-1854)", specifically section 9D. Briefly, the experiments measured the bath temperature, start and end pressures, and "cooling constant" (Joule-Thomson coefficient), and those were used to fit coefficients in Rankine's equation of state for air p = f(V,T), which would allow the use of air for a 'perfect gas thermometer'.

As a consequence, it became possible to define a temperature scale that is independent of the choice of body used as a thermometer, just as the efficiency of a heat engine is independent of the choice of working fluids.
 
  • #5
Thank you very much for your explanation.
 

1. What is the Joule Thomson effect?

The Joule Thomson effect is a phenomenon in thermodynamics where a gas experiences a change in temperature when it is forced through a valve or porous material at a constant enthalpy and with no heat exchange with its surroundings.

2. How does the Joule Thomson effect differ from other thermodynamic processes?

The Joule Thomson effect is unique in that it involves a change in temperature without any heat exchange. Other thermodynamic processes, such as isobaric, isochoric, and adiabatic processes, involve some form of heat exchange.

3. What is adiabatic free expansion?

Adiabatic free expansion is a type of process in which a gas expands into a vacuum without any heat exchange with its surroundings. This process is also known as Joule Thomson free expansion.

4. How is the Joule Thomson effect derived?

The Joule Thomson effect can be derived by applying the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. By setting the work done to zero in the case of adiabatic free expansion, the resulting equation can be manipulated to derive the Joule Thomson coefficient.

5. What are some practical applications of the Joule Thomson effect?

The Joule Thomson effect has many practical applications, including in refrigeration systems where it is used to cool gases by expanding them. It is also used in gas separation processes, such as in the production of liquefied natural gas, and in gas pressure regulation systems.

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