# Open System Carnot Efficiency

1. Jan 4, 2012

### ShamelessGit

1. The problem statement, all variables and given/known data
The original is in German, but I will try my best to translate.

A power generator uses the temperature difference between surface ocean temperature and sea bottom temperature (27C and 6C) to generate electricity. The power outage is 50kW at 10% of the Carnot efficiency. The sea water that is pumped up is warmed from 6 C to 7 C. How much mass per second must be pumped from the ocean floor for this process to occur?

The teacher solved this a few weeks ago and I remember that it turns out that the mass necessary actually goes down if you decrease its temperature increase as it goes through the process (for example if it went from 6C to 6.5 instead of 7). I thought this was counter-intuitive, so I tried to solve it again after Christmas break and I don't get the same result.

2. Relevant equations

kg/s(Δh) = Q/s + Power
Δh/s = C(kg/s)ΔT
Carnot efficiency = 1 - Hot/Cold

3. The attempt at a solution

I'm pretty sure this solution is wrong but I don't know why. The Carnot efficiency is 1- 279/300 = .11, and ten percent of that is .011. I figure the energy being taken from the surface water is responsible for heating the deep sea water and for the 50kW, so I stuck a minus on the P. Also, the heat taken in (Q/s) times the efficiency is supposed to be the work you get out, so P/ε = Q/s = 50kW/.011 = 4545kW of heat from the Ocean. Q - P kg/s(Δh) = 4495kW. Then I figure you just divide both sides by the change in enthalpy to get the mass stream, which means that kg/s is inversely proportional to the temperature increase, which is the opposite of expected.

Plz help. An explanation for why the mass necessary decreases if the temperature increase does would be nice too.