Question

An inventor claims to have developed a wonderful new heat engine that operates with a relatively cool (and therefor nonpolluting) flame at 190 degrees Celcius, and discharges waste heat to the environment at 20 C. His promotional literature advertises that 45 percent of the fuel energy is converted into useful work. Calculate the maximum efficiency that can be expected for such an engine. (If your answer is 45 percent, enter .45) (Is he scamming you or not?)

Answer 1

Answer:

0.367, he is a scammer.

Explanation:

We can calculate the maximum efficiency of a heat engine using both its hot and cold temperatures, which in our case are $T_c=20C=293K$ and $T_h=190C=463K$, with the formula:

$\eta_M=1-\frac{T_c}{T_h}$

So for our case we have:

$\eta_M=1-\frac{293K}{463K}=0.367$

Which means a maximum efficiency of 36.7%, so it cannot have an efficiency of 45% and this "inventor" is scamming people.