Quote by eaboujaoudeh
for isentropic expansion and compression in ICEs we use the same principle u used to find the first 2 works.
we use : W= (PoVoPoVo/4)/(1k) k=Cp/Cv. for isentropic adiabatic compression or expansion.

Where do you get this? It works for BC but not DA
Generally, for reversible adiabatic paths:
(1) [tex]W = K\frac{V_f^{1\gamma}  V_i^{1\gamma}}{1\gamma}[/tex]
where [itex]K = PV^\gamma[/itex]
This is just the integral [itex]\int dW[/itex] where [itex]dW = dU = PdV = KV^{\gamma}dV [/itex] (dQ=0)
Since for DA [itex]P_f = 32P_i[/itex] and [itex]V_f = V_i/8[/itex] the numerator in (1) is simply:
[tex]P_fV_f  P_iV_i = 32P_iV_i/8  P_iV_i = 3P_iV_i[/tex]
for BC, [itex]P_f = P_i/32[/itex] and [itex]V_f = 8V_i[/itex] the numerator in (1) is simply:
[tex]P_fV_f  P_iV_i = 8P_iV_i/32  P_iV_i = 3P_iV_i/4[/tex]
How did u know the gas was monoatomic?

Apply the adiabatic condition [itex]PV^\gamma = constant[/itex] to one of the adiabatic paths and solve for [itex]\gamma[/itex].
AM