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On a cold day, where the outside temperature is 10degreesC, a room in a house is being heated from 10degrees to 20degrees. The volume of the room is 20m^3 and the atmospheric pressure is 101kPa. Cv = 3.6R

due to leaks in the room to the outside the pressure remains constant. I need to prove that the energy after the room has been heated is the same as the energy in the room before the heating.

What i did to solve this was calculate the energy before and the energy after and showed that they were equal.. can someone recommend a better path to prove this?

The next part of the question asks me to calculate the heat input to reach 20degrees in the room at this constant pressure.

For this; i thought i could use dQ = NCvdt + NRdt; however that answer is off from the answer provided in the back of the book by 5kJ or something to that extent(the answer is supposed to be 323kJ).. can anyone toss me a few hints?

Thanks a lot in advance!