Steam heating system transfers heat to a room (Thermodynamics)

[tito agiffaz efata]

Homework Statement

A steam heating system is used in winter season, The radiator of a steam heating system has a
volume of 25 liters and is filled with superheated water vapor at 200 kPa and 200C. At this moment both the inlet and the exit valves to the radiator are closed. After a while it is observed that the temperature of the steam drops to 80C as a result of heat transfer to the room air, which is constant at 21C. Assuming the surroundings to be at 0C, determine:

(a) the amount of heat transfer to the room
(b) the maximum amount of heat that can be supplied to the room if the energy released from the radiator is supplied to a heat engine that is driving a heat pump. Assume the heat engine operates between the radiator and the surroundings

Homework Equations

3. The attempt at a solution

I'm not very sure about the 2nd part (part b) ._.

I'm also not quite sure about my answers, partly because the question included data about the surrounding temperature (21C) and I did not use it in my calculations...

 

[Chestermiller]

It's very hard to read your handwriting. Please make more legible. Also, should you assume the surroundings are at 21 C for part b?