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

AI Thread Summary
To find the final temperature of methane gas expanded adiabatically and reversibly from 550K and 5 bar to 1 bar, the initial volume can be calculated using the ideal gas law. The relationship PV^γ = constant allows for the determination of the final volume, as the initial and final pressures are known. Once the final volume is established, the work done during the expansion can be calculated by integrating pressure with respect to volume. This process will ultimately lead to the calculation of the final temperature. Accurate application of these thermodynamic principles is essential for solving the problem.
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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