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**1. An ideal heat engine (HE) is used to drive a reversible heat pump (HP) as shown in figure**

below. The HE takes in Q1 heat units at T1 and rejects Q2 at T2. The HP abstracts Q4 from the sink at T4 and discharges Q3 at T3. Develop an expression for the ratio Q4/Q1 in terms of the four temperatures (T1, T2, T3, & T4)

below. The HE takes in Q1 heat units at T1 and rejects Q2 at T2. The HP abstracts Q4 from the sink at T4 and discharges Q3 at T3. Develop an expression for the ratio Q4/Q1 in terms of the four temperatures (T1, T2, T3, & T4)

**2.I have sourced some equations for work from elsewhere, but I am unfamiliar with these equations for work as I have not seen them in any of my textbooks or lecture notes. I don't know if the equations are correct, I guess what I'm looking for is confirmation that they are correct and some explanation or reference source so I can understand how these equations were derived.**

Thanks