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.
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:
Qtot = Cp*((T3-T2) + (T1 - T4)
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 Qtot<0