# 2nd law of thermodynamics problems - help

1. Feb 20, 2010

### taureau20

2nd law of thermodynamics problems - help!!

1. The problem statement, all variables and given/known data

See the figure. Q's denote heat transfers while W denotes work supplied by heat engine to heat pump.
(HE denotes heat engine and HP denotes heat pump.) A heat engine operates as shown in figure with an efficiency half of its appropriate Carnot efficiency and drives a heat pump which uses river water (at temperature T4) to warm a room in which the temperature is to be maintained at T3.
Assuming that a temperature difference of 11.1 degree C exists between the working fluid and the river water on the one hand, and the required room temperature on the other, and assuming the heat pump to operate on the reversed Carnot cycle with a COP (coefficient of performance) of 50% of the ideal COP, find the heat input to the heat engine per unit heat output from the heat pump. Why is direct heating thermodynamically more wasteful?

Ans.: 0.79 kJ/kJ

2. Relevant equations

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COP of heat pump = T2/(T2-T1) where T1 is the higher temperature and T1 the lower temperature.

3. The attempt at a solution

I can solve the problem but I am not able to understand what is meant by:

"Assuming that a temperature difference of 11.1 degree C exists between the working fluid and the river water on the one hand, and the required room temperature on the other"

Just let me know what is meant by this and I will be able to solve the problem. Thanks!!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Feb 21, 2010