# Thermodynamics - Carnot cycle

## Homework Statement

An ideal gas is taken through a Carnot cycle. The
isothermal expansion occurs at 250°C, and the isothermal
compression takes place at 50.0°C. The gas takes in 1 200 J
of energy from the hot reservoir during the isothermal
expansion. Find (a) the energy expelled to the cold reservoir
in each cycle and (b) the net work done by the gas in
each cycle.

## The Attempt at a Solution

Qh=1200J.

Qh-W=Qc (absolute values)

e(Carnot)=(523-323)/523= 61.9 %
(corrected my typo from before)

Therefore Qc= .381(1200J)=457J

and W = 1200-457=743J

Not the correct answer. Qc = 741 according to the solutions manual.

ps. Latex seems to be bugged, didn't work in "preview post" mode.

Last edited:

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TSny
Homework Helper
Gold Member
e(Carnot)=1-(523/323)= 61.9 %
Hello. Check this calculation.

Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.

SteamKing
Staff Emeritus
Homework Helper
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.
That's not the problem. Check the numbers. Remember, you are looking for a difference of 2 joules.

Give me another hint, please. I still don't know what I'm doing wrong :). Is my logic even sound?

TSny
Homework Helper
Gold Member
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.

e = (523-323)/523 is correct. But this does not equal .619

• 1 person
what?! How did I miss that, I re-did it like 3 times :/. Thank you though.

TSny
Homework Helper
Gold Member
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.

Also, to get the anwer of 741 J it appears that you should convert to Kelvin by adding 273.15 rather than 273.