Irreversible Adiabatic Expansion (Physical Chemistry)

[djh101]

Homework Statement

Consider the adiabatic expansion of .553mol of an ideal monatomic gas with C_V,m = 3R/2. The initial state is described by P = 6.25bar and T = 306K. Calculate the final temperature if the same gas undergoes an adiabatic expansion against an external pressure of P = 1.25bar to a final pressure P = 1.25bar.

Homework Equations

C_VΔT = -P_extΔV

The Attempt at a Solution

I need to find ΔT. P, V, and T are all variables, though, so I can't find ΔT because I don't know ΔV. What do I do?

 

[Chestermiller]

Use the ideal gas law to express the final volume algebraically in terms of the final temperature. Substitute this into your equation. The final temperature will be on both sides of the resulting equation. Collect terms involving the final temperature, and solve for it.

 

[djh101]

A little bit of annoying algebra, but I got it. Thank you very much.