The radiator of a steam heating system has a volume of 15 litres and is filled w
ID: 2996283 • Letter: T
Question
The radiator of a steam heating system has a volume of 15 litres and is filled with superheated vapour at 300kpa and 200 degrees celcius. At this moment both inlet and outlet valves to the radiator are closed. Determine the amount of heat that will be transferred to the room when the steam pressure has dropped to 100kpa. Also show the process on a P-v diagram with respect to saturation lines clearly labeling both state points. Suppose this process took one hour to occur, furthermore suppose the radiator is located in a room where the net rate of heat loss from the room is 100kJ/hr. Given this situation, determine wheter the temperature of the air in the room will increase, decrease or stay the same.
Explanation / Answer
If we assume that the radiator does not expand or contract significantly with the temperature change, we have is a constant volume process. We can find the entropy change from the initial state, where we are given the temperature and pressure and the final state where we know the temperature and we also know that the specific volume will be the same as it is at the initial state. We can also use the information on the radiator volume to find the system mass.
At the initial state of 200 kPa and 150oC, we find the following properties from Table A-6 on page 920: v1 = 0.95986 m3/kg and s1 = 7.2810 kJ/kg?K. From Table A-4 on page 916, we see that, at the final temperature T2 = 40oC, the specific volume, v2 = v1 is between vf(40oC) = 0.001008 m3/kg and vg(40oC) = 19.515 m3/kg. Thus the final state is in the mixed region. We find the final quality from the following equation.
We can then use this quality to find the final entropy.
To find the total entropy change we have to find the system mass. We can find this from the radiator volume and the initial specific volume.
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