Heat engine/thermal efficiency question

[apaerie]

Homework Statement

The figure shows the cycle for a heat engine that uses a gas having gamma =1.25. The initial temperature is T₁=300K, and this engine operates at 20 cycles per second. What is the engine's thermal efficiency?

[URL]http://session.masteringphysics.com/problemAsset/1074111/3/knight_Figure_19_54.jpg[/URL]

Homework Equations

[PLAIN]http://upload.wikimedia.org/math/7/a/1/7a19ba3fdf776ed7bf92a998cb72996c.png=W[SUB]out[/SUB]/W[SUB]in[/SUB]

[PLAIN]http://upload.wikimedia.org/math/7/a/1/7a19ba3fdf776ed7bf92a998cb72996c.png=1-Q[SUB]c[/SUB]/Q[SUB]H[/SUB]

The Attempt at a Solution

The first question had asked what was the power output of the engine and I managed to get the correct answer for that, so I'm very sure that my values for Q12, Q23, and Q31 are correct. Since Q23 was a positive value, I figured it was the work put in. I then used the power output that I had calculated and divided it by Q23, multiply by a hundred, which gave me 18% which turned out to be wrong.

I then tried the second equation and using the same value (Q23) for Q_H and adding the absolute values of Q12 and Q31 together to get Q_c, divide Q_c by Q_H, and subtracted the result from 1. It still turned out to be 18%, which I already knew was wrong.

So I'm not sure what I'm doing wrong here. Any feedback would be greatly appreciated.

 

[Redbelly98]

Welcome to Physics Forums.

You're approach looks entirely correct. If this is being checked by submitting online, and you don't know what the "correct" answer is, then there might be some issue with significant figures, or rounding error -- in which case you got the right answer, but it isn't registering.

Can you post your calculations of W₁₂, W₂₃, and the three Q's?

EDIT: I have now worked out the problem, and it is quite different than 18%, so I suspect you calculated the Q's incorrectly. If you show your work, I could help find the error.

 

[apaerie]

Welcome to Physics Forums.

You're approach looks entirely correct. If this is being checked by submitting online, and you don't know what the "correct" answer is, then there might be some issue with significant figures, or rounding error -- in which case you got the right answer, but it isn't registering.

Can you post your calculations of W₁₂, W₂₃, and the three Q's?

EDIT: I have now worked out the problem, and it is quite different than 18%, so I suspect you calculated the Q's incorrectly. If you show your work, I could help find the error.

I figured it out. You're right, I did miscalculate one of the Q's. At the beginning, I calculated Q_H (or Q23) to be 303J but I know now that was where I went wrong, so I managed to get the right answer now. Thanks for all your trouble :)