I was reading about the Carnot engine, and I stumbled upon this forumla:

Carnot efficiency = 1 - (QH-QL)/QH = 1 - (TH-TL)/TH

Where QH is the heat input, QL is the heat output, TH is the input temperature, TL is the output temperature.

The book says that TH is proportional to QH, and TL is proportional to QL, but it does not state why. Well it seems common sense that you have more heat input if the source is hotter, but is there a more scientific explanation? Or is it just a finding from Carnot's observations?
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 I'm not much of a specialist, but I think the fact can be deduced easily while one works through the derivation of carnot efficiency. Here is the link from wikipedia. http://en.wikipedia.org/wiki/Carnot_...d_significance
 It's true by definition of thermodynamic temperature, T. You can show from the second law of thermodynamics that all Carnot engines have the same efficiency, independently of working substance, so their efficiencies can depend only on the temperatures TH and TC. It was, I believe, the idea of William Thomson (Lord Kelvin) to define temperature such that $$\frac{T_H}{T_C}=\frac{Q_H}{Q_C}$$ in which QH and QC are the heat input and heat output of a Carnot engine. By taking the special case of an ideal gas as working substance in a Carnot engine, it is easy to show that the thermodynamic temperature as defined above, is equivalent to temperature defined by pV = nRT for a gas at limitingly low density. Obviously what I've written is highly condensed. It is spelled out in detail in old-fashioned textbooks such as Zemansky.

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 Quote by titaniumpen I was reading about the Carnot engine, and I stumbled upon this forumla: Carnot efficiency = 1 - (QH-QL)/QH = 1 - (TH-TL)/TH Where QH is the heat input, QL is the heat output, TH is the input temperature, TL is the output temperature. The book says that TH is proportional to QH, and TL is proportional to QL, but it does not state why. Well it seems common sense that you have more heat input if the source is hotter, but is there a more scientific explanation? Or is it just a finding from Carnot's observations?