A simple thermodynamic analysis that might be of interest to you is the heating

Question

A simple thermodynamic analysis that might be of interest to you is the heating of a room in your house with a regular electric heater. Let's take an arbitrary size of dimensions 3.5 m (side), 5.0 m (side), and 3.0 (height). As you are aware the doors on house rooms are not airtight. There is always air leaks from underneath the door. An interesting question is to predict how long it will take to heat up to a desired temperature after turning the heater on. Let's assume you heater dissipates power at a rate of 1.5 kilowatts and that the initial temperature of the room is 10 degree C (typical temperature when you get home after leaving the heater off all day). To simplify things a little let's assume that air behaves as an ideal gas with C^degree_p = 29 J/mol K. The first question that we would like to answer what is the temperature in the room after turning the heater on for five minutes? If there are leaks in the room through the door, then it is very likely the pressure in the room will stay constant to whatever the atmospheric pressure is. The other possibility is that seal the door with a typical under the door rubber seals you can buy in home supplies store. In that case we will not have air leaks in the room. Solve the problem again, but assuming that there are not air leaks in the room for at least five minutes and find the temperature at that time.

Explanation / Answer

The volume of room = 3.5 X 5 X 3 = 52.5 m^3

Density of air = 1.225 Kg / m^3

Mass of air = 1.255 x 52.5 = 65.89 Kg

Heat produced by heater = power X time = 1.5 X10^3 watts X 5 X 60 = 450 Kjoules

Heat gained by air = Mass of air X specific heat of air X change in temperature

1 mole of air = 28.89 Grams

65.89 Kg = 2.28 Kilomoles

450 X 10^3 = 2.28 X 10^3 X 29 X (T2-10)

6.805 = T2-10

T2= 16.805 C

we need to know the heat losses due to leakage to know the exact temperature

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