Calculate gas outlet temperature and heating or cooling from a Joule-Thomson coefficient and pressure change, or solve the coefficient from inlet and outlet conditions.

Positive coefficients cool during a pressure drop; negative coefficients warm.

Constant-coefficient estimate for isenthalpic throttling. Use gas-specific property data for large changes or phase changes; this is not equipment design guidance.

Joule Thomson Effect Formula

The following formula is used to calculate the final temperature of a gas after expansion through the Joule Thomson effect.

Tf โ‰ˆ Ti + ฮผ ร— (Pf - Pi)

Variables:

  • Tf is the final temperature of the gas (K)
  • Ti is the initial temperature of the gas (K)
  • ฮผ is the Joule Thomson coefficient (K/bar)
  • Pi is the initial pressure of the gas (bar)
  • Pf is the final pressure of the gas (bar)

For a constant-coefficient estimate, subtract the initial pressure from the final pressure, multiply this signed change by the Jouleโ€“Thomson coefficient, and add the initial temperature. A positive coefficient gives cooling during a pressure drop. Use consistent pressure units and temperature-difference units; use positive absolute pressures in this calculator.

What is the Joule Thomson Effect?

The Joule Thomson effect describes the temperature change of a real gas or liquid when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. This process, called a throttling process or Joule Thomson expansion, is an isenthalpic process (occurs at constant enthalpy). The effect is used in refrigeration and liquefaction of gases.

How to Calculate Final Temperature using Joule Thomson Effect?

The following steps outline how to calculate the final temperature of a gas after expansion using the Joule Thomson effect.

  1. First, determine the initial temperature of the gas (Ti) in kelvin.
  2. Next, determine the initial pressure of the gas (Pi) in bar.
  3. Next, determine the final pressure of the gas (Pf) in bar.
  4. Next, determine the Joule Thomson coefficient (ฮผ) in kelvin per bar.
  5. Next, use the constant-coefficient estimate Tf โ‰ˆ Ti + ฮผ * (Pf – Pi).
  6. Finally, calculate the final temperature (Tf) in kelvin.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial temperature of the gas (Ti) = 300 K

Initial pressure of the gas (Pi) = 10 bar

Final pressure of the gas (Pf) = 1 bar

Joule Thomson coefficient (ฮผ) = 0.25 K/bar. The estimate is Tf โ‰ˆ 300 + 0.25 ร— (1 โˆ’ 10) = 297.75 K, a cooling of 2.25 K.