A room 4x5x6 meter is heated by a baseboard resistance heater. We want the heater to raise the room temperature from 7 to 23 deg C in 15 minutes. There are no heat losses from the room, and specific heat may be assumed constant. Power costs 15 cents per kilowatt hour.
What power is required to heat the room?
How much will it cost for one 15 minute episode of heating?
What is the average length between adjacent air molecules during this process?