# Homework Help: Thermodynamics engine question

1. Nov 17, 2005

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 doesnt hold, i.e.:
50 % > 54 % is not true.​

Is this the correct way to do this problem?
Thanks

2. Nov 17, 2005

### Physics Monkey

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

3. Nov 17, 2005

Thanks very much

4. Nov 18, 2005

### Andrew Mason

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