What is the efficiency of a Carnot engine and the effectiveness of a heat pump?

[sora1607]

Homework Statement

A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is |QH|. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir at a temperature T`. The amount of heat removed from the 842-K reservoir is also |QH|. Find the temperature T`.

Homework Equations

Qc/Qh = Tc/Th
Qh = W + Qc

The Attempt at a Solution

This problem was posted before with no solution and now I'm running into the same problem. I've attempted the problem by first getting Qh=2Qc for the carnot engine. Then this input heat + W is used to operate a heat pump. So I got Qh + w = 2Qc. I'm stuck starting here. I'm not sure how this input heat would fit into the heat pump cycle.

The answer is suppose to be 1263

 

[rock.freak667]

For the Carnot Engine section, how do you find the efficiency of the engine? (express W in terms of Qh).

For the heat pump section, we are inputting W to move Qh to some other reservoir Q (at temp T'). How do you find the effectiveness of a heat pump?