Carnot Efficiency: Qh/Ql=Th/Tl Explained

[John Pang]

Another question, according to catnot efficiency, Qh/Ql=Th/Tl .Can anyone help explain how is this equation derived? It is really frustrating as my textbook doesn't explain this.

 

[drvrm]

according to catnot efficiency, Qh/Ql=Th/Tl .Can anyone help explain how is this equation derived? It is really frustrating as my textbook doesn't explain this.

Carnot cycle abcd ; ab and cd are the isothermals
The heat absorbed and rejected by the system takes place during isothermal processes
Q is of the form
Heat absorbed /rejected in isothermal paths -NRT2 ln (Vb/Va)

Or NRT1. ln (Vd./Vc)

so Q1/Q2 = (T1/T2) . the ratio of the Volume factors
But if one applies the adiabatic equations as the points b,c and a,d are connected adiabatically thereby one can get the equality of the volume factors and they cancel out
thats why

Q1/Q2 = -T1/T2 or Q 1/T1 +Q2/T2 = 0

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/img361.png
see for details <http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node21.html>

 

[John Pang]

Thx. So it can be easily derived from the equations U=3/2nRT , and change in U= Change in Q - W, right?

 

[drvrm]

Thx. So it can be easily derived from the equations U=3/2nRT , and change in U= Change in Q - W, right?

i think so as in isotherms dU =0 and Q= W (integral of PdV)
and in isotherms P.V^gamma =constant/ or TV ^(gamma-1) = const.