What is the Final Temperature of Methane Gas After Adiabatic Expansion?

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SUMMARY

The final temperature of methane gas after adiabatic expansion from 5 bar to 1 bar can be determined using the relation PVγ = constant. Given the initial conditions of 550K and 5 bar, the final volume can be calculated by rearranging the equation with known pressures. The final temperature can then be derived using the ideal gas law and the specific heat ratio for methane, which is approximately 1.31.

PREREQUISITES
  • Understanding of the ideal gas law
  • Knowledge of adiabatic processes in thermodynamics
  • Familiarity with the specific heat ratio (γ) for gases
  • Basic calculus for integrating pressure with respect to volume
NEXT STEPS
  • Study the derivation of the adiabatic process equations
  • Learn how to calculate specific heat ratios for different gases
  • Explore the application of the ideal gas law in thermodynamic processes
  • Investigate numerical methods for solving thermodynamic equations
USEFUL FOR

Students and professionals in thermodynamics, chemical engineering, and anyone involved in gas expansion processes will benefit from this discussion.

cruckshank
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Methane gas at 550K, 5 bar is expanded adiabatically and reversibly to 1 bar. Find the final temperature of the gas.

I have made little progress with this...

I've calculated the initial volume, and that is all so far. Obviously to find the work usually I'd integrate pressure with respect to volume, after substituting PVγ=const but I can't do this because the final volume isn't available to me...

Help would be appreciated!
 
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Using PV^gamma = constant you can easily calculate the final volume as P(initial), P(final) and V(final) are known.
 

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