Question

An inventor claims to have developed an engine which takes in 11times10^(7)J at 400K rejects 5times10^(7)J at 200K and delivers 16.67kW hours of work.Would you advise investing money in this project?

Answer 1

Solution.

$Q_1=11\sdot10^7J;$

$T_1=400K;$

$Q_2=5\sdot10^7J;$

$T_2=200K;$

$\eta=1-\dfrac{T_1}{T_2};$

$\eta=1-\dfrac{400K}{200K}=0.5 or 50\%$ ;

$\eta=\dfrac{Q_1-Q_2}{Q_1};$

$\eta=\dfrac{11\sdot10^7J-5\sdot10^7J}{11\sdot10^7J}=0.55 or 55\%$ ;

By Carnot's theorem, no engine can be more efficient than a carnot engine, or: Efficiency(carnot) > Efficiency(hypothetical)​and in this case, it doesnt hold, i.e.: 50 % > 55 % is not true.​

Answer: You should not invest in such a project, it is not real.