joe_cool2
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Homework Statement
A heat engine uses the closed cycle shown in the diagram below. (Figure 1) The working substance is n moles of monatomic ideal gas. Find the efficiency of such a cycle. Use the values for pressure and volume shown in the diagram, and assume that the process between points 1 and 3 is isothermal.
Homework Equations
pV=nRT
efficiency = Wout/QH
The Attempt at a Solution
We know that T3 and T1 are on an isotherm, and so are both exactly 3 times T2. So, the absolute value of ΔT is 2 times T2. The reason I refer to the absolute value here is because the sign of ΔT for different processes will be different.
Wout = nRT*ln(V1/V3) - pΔV
So, Wout = nRT*ln(V1/V3) - nRΔT
QH= nRT*ln(V1/V3) + nCvΔT
So the efficiency is:
3nRT2*ln(V1/V3) + 2nRT2 / 3nRT2*ln(V1/V3) + 2nCVT2
Then the idea is to cancel out all the n's and T2's. All the rest are knowns. I get a value of 84.1%. There's definitely something very wrong about my approach.
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