[cseil]

Hello,
I want to demonstrate that the efficiency of a heat engine is
η = 1- T2/T1.

The cycle is made of:
1) isothemal expansion (rev.)
2) adiabatic expansion (rev.)
3) iisothermal compression (rev.)
4) adiabatic compression (rev.)

and it works at two temperatures (T1,T2 and T1 > T2)

I calculated the heat involved during the step 1 and 3.

q1=RT1ln(V2/V1)
q3=RT2ln(V4/V3)

The efficiency is
η=w/q1=q1-q3/q1 = 1-q3/q1.

Now I have:

[tex]\eta = 1 - \frac{T2}{T1} \frac{ln(V4/V3)}{ln(V2/V1)}[/tex]

and I don't understand how to get rid of the last part of the equation.
Hint?

[orthoformate]

IF you have 20 minutes, watch these videos: https://www.khanacademy.org/science/physics/thermodynamics/laws-of-thermodynamics/v/proof-volume-ratios-in-a-carnot-cycle

https://www.khanacademy.org/science/physics/thermodynamics/laws-of-thermodynamics/v/efficiency-of-a-carnot-engine

the second one should be great for you. The first one is a derivation

hope this helps : )

[cseil]

Thank you, that was helpful!