How to prove the work done by an ideal gas with constant heat capacities during a quasi-static adiabatic expansion is equal to W=-C(Ti-Tf).
I know we can use 1st law thermodynamic, Q=U-W where, Q = Heat, U = Internal Energy, W = Work
However, my derivation/prove leads to wrong and mess-up equation.
W = ΔU W = -PdV W = -(K/V^Y)*dV W = -K∫(1/V^Y)*dV W = -K[V^(1-Y)/(1-Y)]*∫dV W = -(K/(1-Y))[Vf^(1-Y) - Vi^(1-Y)] W = -(K/(1-Y))[Vf^(-Y)*Vf - Vi^(-Y)*Vi] W = -(1/(1-Y))[((Vf*K)/(Vf^Y)) - ((Vi*K)/(Vi^Y))]
Then i confuse.