Carnot Reversible Machine: Exploring the Impact on 2nd Law of Thermodynamics

[Chacabucogod]

I was reading Cengel's thermodynamics and noticed that he uses a thought experiment to show that there is no machine that is more efficient than the Carnot reversible machine. He says that both a reversible machine and an irreversible machine are connected to high and low temperature deposits, and that they both receive Qh from the high temperature deposit. He next assumes that the irreversible machine is more efficient than the Carnot machine, and reverses the Carnot machine so that it works as a "refrigerator". The refrigerator is going to be providing Qh to the hot deposit and the irreversible machine will receive Qh so that the deposit can be taken away and both of the machines connected. Then the machines would not have two deposits to complete the cycle and it would not agree with the second law.

Now if I don't assume that the Carnot machine is less efficient than the irreversible machine and reverse it wouldn't the second law be broken too? Or would the Qh that the Carnot machine is providing be less than the required by they second machine?

Thank you

 

[DrClaude]

The refrigerator is going to be providing Qh to the hot deposit and the irreversible machine will receive Qh so that the deposit can be taken away and both of the machines connected. Then the machines would not have two deposits to complete the cycle and it would not agree with the second law.

Another way to see it is with both reservoirs connected, and the combination of the heat engine and the Carnot refrigerator as one machine. You would then get a heat engine that transfers heat from the cold reservoir to the hot one, without any external input. This is an obvious violation of the 2nd law.

Now if I don't assume that the Carnot machine is less efficient than the irreversible machine and reverse it wouldn't the second law be broken too? Or would the Qh that the Carnot machine is providing be less than the required by they second machine?

Remember that there is "work" between the two machines. If the heat engine's efficiency is equal or less than a Carnot engine, then the work produced by it, when supplied to the Carnot refrigerator, will lead to a transfer of heat from cold to hot reservoirs (by the Carnot refrigerator) that is less than the consumption of heat from the hot reservoir by the heat engine.