Reverse Carnot Engine (Heat Pump)

[mrmonkah]

Homework Statement

A house is heated by means of a carnot engine operating in reverse (Heat Pump). The outside Temperature (Tc) is 270k, and the required inside temperature (Th) is 300k. If heating the house to this temperature normally requires 10kW of electrical heating, how much power is consumed by the carnot heat pump to maintain the same temperature?

Homework Equations

n = $$\frac{W}{Q1}$$ = 1 - $$\frac{Tc}{Th}$$ = 0.1

The Attempt at a Solution

I'm really having problems labelling each of the 'heat exchanges. I have Tc as the cold reservoir and Th as the hot reservoir. Should my heat from Tc be Q1 and then work is done, followed by Q2 into the hot reservoir? Then use the relevant equations to get the power consumption of the engine?

 

[darkys]

Yes, that is correct. You have correctly identified the two heat reservoirs. The Carnot engine is operating in reverse, so heat is being drawn from the cold reservoir at temperature Tc and transferred to the hot reservoir at temperature Th. The power consumption of the engine will be calculated by using the equation n = \frac{W}{Q1} = 1 - \frac{Tc}{Th}, where W is the work done by the engine, and Q1 is the heat transferred from the cold reservoir.