Thermodynamics Problem Clarification

[neelakash]

Homework Statement

Show that if the Clausius statement of the 2nd law were not true a violation of Kelvin Planck statement would be possible.

Homework Equations

The Attempt at a Solution

My attempts: Please check it and confirm if I am correct.

Clausius Statement - States that it is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower temperature body to a higher temperature body.

Kelvin-Planck Statement - States that no system can produce a net amount of work while operating in a cycle and exchanging heat with a single thermal energy reservoir.

let there be a heat pump HP which takes Q2 heat from TL and delivers it to TH(Clausius statement)
Let us consider another Heat engine that takes heat a source TH and delivers a wet work out put W_net and rejects Q2 heat to sink.

Now we can remove T(LOW), and feed the Q2 heat from HE to HP

Now considering HE+HP as a single heat engine, we see it produces a net work Wnet while exchanging heat with a single energy reservior(KelvinP statement)

 

[berkeman]

This thread appears to be a re-post of this:

https://www.physicsforums.com/showthread.php?t=173388

Please do not double-post questions. This thread here is locked for now.