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

.5m (side), 5

.0 m (side), and 3

.0 (height)

. As you are aware the doors on house rooms arenot airtight

. There is always air leaks from underneath the door

. An interesting questionis to predict how long it will take to heat up to a desired temperature after turning theheater on

. Let’s assume you heater dissipates power at a rate of 1

.5 kilowatts and thatthe initial temperature of the room is 10°C (typical temperature when you get home afterleaving the heater off all day)

. To simplify things a little let’s assume that air behaves as anideal gas with C◦p = 29 J/mol K

. The first question that we would like to answer what is thetemperature in the room after turning the heater on for five minutes? If there are leaks inthe room through the door, then it is very likely the pressure in the room will stay constantto whatever the atmospheric pressure is

. The other possibility is that seal the door with atypical under the door rubber seals you can buy in home supplies store

. In that case we willnot 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

.