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## Homework Statement

A Carnot engine using a gas operates between 2 reservoirs of temperatures 1000K and 280K. The work output per cycle is 1kJ.

a) What is the efficiency?

b) What is the entropy change of the gas per cycle due to the heat transfer at the hot reservoir?

## Homework Equations

[tex] \eta_{carnot} = 1 - \frac{Q_{1}}{Q_{2}} = 1 - \frac{T_{1}}{T_{2}} [/tex]

[tex] \Delta S = \int \frac{dQ}{T} [/tex]

[tex] \Delta U = W_{on} + Q_{in} [/tex]

## The Attempt at a Solution

a) Seems easy enough, I got 72%.

b) I think you just use the entropy formula above, which goes to S = Q_in / T_2 (never used Latex before, and wasn't working here - don't have time to work out why!). If internal energy, U, is zero then heat in equals negative work done on the gas (ie. -1kJ) due to the 1st law. In that case I get the change in entropy to be 1.. which just doesn't seem right. Can anyone comment/help?

Thanks!