This thread needs more science.
Commander Data's living room heating problem:
System: living room
Initial temperature: T1
Final (desired) temperature: T2>T1
If we assume that the room is perfectly insulated, then according to the 1st law of thermodynamics: ΔU=Q, where ΔU is the change in the internal energy of the room and Q is the amount of heat we introduce to the system to increase the temperature from T1 to T2. So basically the energy of the room increases by Q.
However in reality things aren't that simple.
The room is not perfectly insulated and we have to take into account the losses of energy to the environment (through the walls, windows etc). What is needed is an energy balance:
(Energy into the room) = (Energy out of the room) + (Energy Accumulation)
I don't want to get into details and start writing differential equations (for obvious reasons
), but I think one could simplify.
Assuming that we have a heating system with a thermostat programmed to our desired temperature T2, when we turn it on, the room will start warming up (i.e. the rate of heat going into the room will be greater than the rate of heat loss). Therefore the energy of the system increases (we have positive Energy Accumulation). Once the temperature reaches T2 a steady state will be established (ignoring small temperature fluctuations etc). From that point on, Energy Accumulation = 0, i.e. the energy of the system will remain unchanged.
It cannot be a closed system since we are introducing heat into it in the first place.
Correct about the entropy, it always increases etc but I don't think it is something to worry about in this case.