# Efficiency given two temperatures

Not sure what formula to use for this question? I am new to physics and the regular efficiency formula doesn't seem like the one I should be using. I was thinking the carnot efficiency, since it claims it is a "perfect" power plant:

I build the perfect power plant that operates between 350 deg.C and 20 deg.C. What is its efficiency?

## 2 Answers

You have to use the formula $$\eta=1-\frac{T_1}{T_2}$$

Well, if you want to maximize the efficiency (work/heat transfer), you can use the Carnot efficiency, which yngabl already pointed out is $\eta=1-T_1/T_2$. But one cycle takes an infinite amount of time, and therefore your power output will be zero. If you want to maximize power instead of work you'll have to do an irreversible process, and then the efficiency might be given by the Chambadal-Novikov efficiency $\eta=1-\sqrt{T_1/T_2}$. See https://en.wikipedia.org/wiki/Endoreversible_thermodynamics

• This is interesting. – Sayan Mandal Oct 15 '17 at 3:03