Can Calculating Ocean Bottom Temperature Enable Efficient Heat Engine Operation?

[ruiwp13]

Homework Statement

A haet engine works based on the difference of the temperature at the top and bottom of the ocean. The machine is solar powered and the average solar irradiance is 240W/m^2 and the temperature at the surface of the water is 25ºC. Calculate the temperature at the bottom of the ocean so that the machine debits a power of 0.1MW to a surface area of 10^4 m^2.

Homework Equations

Q=σ*A*T^4(surface)

The Attempt at a Solution

I am stuck in this one... I don't know if it is possible for you to give me some hint. I'm not sure if I need to find the efficiency here, but I'll probably will need it to get the heat at the bottom and maybe trough there get the temperature.

 

[jim hardy]

the machine debits a power of 0.1MW to a surface area of 10^4 m^2.

is sure a roundabout way to phrase what i take to be power balance...

Do you suppose he means "delivers useful work of 10 watts/m² at Carnot efficiency?

If so, it seems to me he's given you both efficiency and T_hot .

 

[Borek]

My bet is that is about efficiency only - you are given energy input and energy output. See if you can follow from here.

Edit: Jim was slightly faster, and we definitely said the same thing.

 

[ruiwp13]

First I want to thank you both for the answer. Yes, I concluded that it was supposed to use the efficiency and I was given Th being Tc the temperature at the bottom. It's done!