Does this engine violating Carnot efficiency deserve investment?

[ChronicQuantumAddict]

Ok, my question is as follows:

An inventor claims to have developed an engine that takes in 10^8 J (Q_in) at a temperature of 400 K (T_2), and rejects 4x10^7 J (Q_out) to a reservoir of Temperatue of 200 K (T_1). The engine delivers 15 kilowatt hours of mechanical work (which = 3600 sec/hour *15 * 10^3 watts = 5.4x10^6 Joules). Would you advise investing money to put this engine on the market?

the way i approached it was to calculate the max efficiency that a carnot engine would have, which is:

efficiency = 1 - T_1/T_2 = 1 - 200/400 = 0.5 or 50%​

Now, using the expression,

Efficiency = Work output/Heat input​

for the hypothetical engine gives. This gave me an efficiency of roughly 54%, and by Carnot's theorem, no engine can be more efficient than a carnot engine, or:

Efficiency(carnot) > Efficiency(hypothetical)​

and in this case, it doesn't hold, i.e.:

50 % > 54 % is not true.​

Is this the correct way to do this problem?
Thanks

 

[Physics Monkey]

I didn't check your number crunching, but you've approached the problem correctly.

 

[ChronicQuantumAddict]

Thanks very much

 

[Andrew Mason]

Ok, my question is as follows:
An inventor claims to have developed an engine that takes in 10^8 J (Q_in) at a temperature of 400 K (T_2), and rejects 4x10^7 J (Q_out) to a reservoir of Temperatue of 200 K (T_1). The engine delivers 15 kilowatt hours of mechanical work (which = 3600 sec/hour *15 * 10^3 watts = 5.4x10^6 Joules). Would you advise investing money to put this engine on the market?

So what is your answer and why?

My reason for not investing (besides the fact that the claim cannot be true as you have shown) would be: where are you going to find a reservoir to output at -73C?

AM