Thread: Another Thermo Question View Single Post
HW Helper
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 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= (PoVo-PoVo/4)/(1-k) k=Cp/Cv. for isentropic adiabatic compression or expansion.
Where do you get this? It works for BC but not DA

(1) $$W = K\frac{V_f^{1-\gamma} - V_i^{1-\gamma}}{1-\gamma}$$

where $K = PV^\gamma$

This is just the integral $\int dW$ where $dW = dU = PdV = KV^{-\gamma}dV$ (dQ=0)

Since for DA $P_f = 32P_i$ and $V_f = V_i/8$ the numerator in (1) is simply:

$$P_fV_f - P_iV_i = 32P_iV_i/8 - P_iV_i = 3P_iV_i$$

for BC, $P_f = P_i/32$ and $V_f = 8V_i$ the numerator in (1) is simply:

$$P_fV_f - P_iV_i = 8P_iV_i/32 - P_iV_i = -3P_iV_i/4$$

 How did u know the gas was monoatomic?
Apply the adiabatic condition $PV^\gamma = constant$ to one of the adiabatic paths and solve for $\gamma$.

AM