# Homework Help: Comparing Carnot efficiency to Stirling efficiency

1. Mar 28, 2013

### WalkTex

1. The problem statement, all variables and given/known data

In the problem, we were to derive work and heat for each leg of the cycle. Then we are asked:

In the definition of the efficiency of this cycle, η =W Qpos , where Qpos is the total positive heat flow to the engine, what is the efficiency of the cycle when Th = 700K and
Tc = 400K? V1 = 0.5 L and V2 = 1.5 L. Compare this efficiency to the efficiency of a Carnot cycle that operates between the same temperature extremes.

2. Relevant equations

Work = integral from Vi to Vf of PdV
W done during cycle = nr(Th-Tc)ln(vf/vi) Derivation here:

http://www.pha.jhu.edu/~broholm/l39/node5.html [Broken]

Q = Cv(Th -Tc) - nRT ln (Vf/Vi)

We are told Cv = 5/2 * R

efficiency of a carnot cycle = 1- Tc/Th

3. The attempt at a solution

I have attempted to get the solution but have come up with a result that is about an order of magnitude too small that i am unable to rectify. It is part c in the attachment.

#### Attached Files:

• ###### stirling.pdf
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Last edited by a moderator: May 6, 2017
2. Mar 28, 2013

### TSny

CV = 5R/2 is the molar heat capacity at constant volume for a diatomic gas. You need to take account the number of moles when using CV. (You didn't specify if the number of moles is given or whether the gas is monatomic or diatomic.)