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## Homework Statement

I was given the Brayton reverse cycle and asked to prove that the total heat is negative (hence the heat pump cools the system).

I was to assume that all the steps are reversible.

## Homework Equations

An ideal diatomic gas.

1st step: adiabatic compression.

2nd step: isobaric heat.

3rd step: adiabatic expansion.

4th step: isobaric heat absorption.

I managed to get to the equation:

Q

_{tot}= C

_{p}*((T

_{3}-T

_{2}) + (T

_{1}- T

_{4})

## The Attempt at a Solution

Since I have two adiabtes there are only two places in the cycle where Q can change - the two isobars I summed the two heata calculated from the Energy differential and managed to get to the equation above for total heat but didn't manage to prove that Q

_{tot}<0