Carnot Heat Pumps: Solving |Q_c|/|Q_h|=T_c/T_h Equation

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    Carnot Heat Pumps
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The discussion revolves around the Carnot engine operating between hot and cold reservoirs at 1684 K and 842 K, respectively. The engine's work is used to power a Carnot heat pump that transfers heat from the cold reservoir to a hot reservoir at temperature T'. The equation |Q_c|/|Q_h|=T_c/T_h is central to solving the problem, with participants exploring the relationship between heat and work. One user calculated that |W| equals half of |Q_h| but expressed uncertainty about their final temperature T' of 1684 K. Clarification on the problem's structure and further guidance on calculations were sought by forum members.
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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`.


|Q_c|/|Q_h|=T_c/T_h
|Q_h|=|W| + |Q_c|


I'm having trouble visualizing this problem. Are there two separate engines? Doing a little rearranging, I was able to get down to |W| = 1/2 |Q_h|. I figure that since there are no values for either heat value or work that they cancel out. I'm just not sure how to proceed. I worked it one way and got my final T` to be 1684 K, but I don't feel too confident about it. Anyone out there know where I should start or if I'm even on the right track?
 
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This was posted earlier. Please don't double post.

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I'm really sorry, I am new to the forum and wasn't sure which category to post it in. Will not happen again.
 

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