Question

One mole of a monoatomic ideal gas expands adiabatically from T= 298.15 K and P = 1 bar against a constant external pressure of0.75 bar. Find the final temperature of the gas, the molar workdone, and the change in the molar entropy for this process.

I understand the process is an irreversible adiabatic so I cannotuse PV^δ=Constant

I Know:

q=0

ΔU=w=Cv(T₂-T₁)

w_{(irreversible)}= -P_extΔV

so, CvΔT=-P_extΔV

Cv=3/2R, PV=nRT

Therefore : 3/2(R)(T₂-T₁) =-P_ext{(RT₂/P_ext)-(RT₁/P)}

I do not know how to solve forT₂

I can finish the rest of the problem if someone could pleaseexplain (step-by-step) how to solve for T₂

Any help would be greatly appreciated.