Fred has a high tech home equipped with precision thermostats and power monitoring equipment, just as you would expect a guy in a physics quiz problem to have. Before Fred arrives home on a chilly day, his TV room is automatically brought up to 68 degrees. The room has only an electric room heater, and when the temperature stabilizes, a total of exactly 1000 watts is flowing into the room.

Fred arrives home and goes into his heated TV room. He switches on two lamps that consume 60 watts of electric power each. He switches on his wide-screen TV that draws 300 watts. The environment outside the room stays precisely the same, which is typical of quiz problem weather.

When the room stabilizes again, how much electric power will be flowing into the room, counting all the devices?

a. Consumption drops to about 700 watts.
b. It stays at 1000 watts.
c. It increases to 1120 watts.
d. It increases to 1300 watts.
e. It increases to 1420 watts.

This is a straightforward energy conservation problem. There are no tricks of computer-controlled thermostats or unstated conditions. So what do you think?

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The answer is (a) Consumption drops to about 700 watts. All the energy going into the light bulbs and the TV end up as room heat, so if Fred had not entered the room and the electrical equipment were turned on, the consumption would have stayed at 1000 watts. The thermostat would have adjusted the heater down to keep the total heat energy input constant. The heater would have provided 580 watts and the TV and light bulbs 420 watts.

Fred, however, is an added heat source. The average person dissipates about 300 watts, produced by burning off Big Macs and tofu. We don’t know if Fred is a dimmer bulb than average or a brighter one, so there is some uncertainty. Air conditioning engineers are much aware of the human heat load. It is an important factor is computing the air conditioning requirement for meeting rooms and auditoriums.

With Fred contributing 300 watts, and the TV and light bulbs contributing 420 watts, the heater will need to contribute only 280 watts to maintain the room temperature. If Fred dresses warmly, his body will have to burn fewer calories to stay warm, so the room heater will have to work a little harder.

Had the problem been posed in the summer, the answer would be much different. Air conditioners operate at various efficiencies, but it takes roughly one watt of electricity to remove three watts of heat. Fred would add 300 watts of heat, and his electrical appliances another 420 watts. Fred’s air conditioner would then have spent about an extra 240 watts to get rid of the extra 720 watts of heat added to the room, for a total of 1960 watts consumed.

The practical implication is that energy efficient appliances and compact fluorescent lights save much less energy in the winter than it seems they do. If you heat with gas and the gas is cheaper than electricity, there will be a some savings. However, if you are running air conditioning in the summer, then energy savings devices save about a third more than it seems they do.

The net energy savings in a year from efficient devices depends upon your specific heating and cooling usage. If you use no air conditioning, you will still gain whatever the energy conservation appliances save during the summer. If you heat only part of your house in the winter, then you will also save whatever energy is saved by energy saving appliances in the unheated portion of your house, such as the energy saved by an efficient water heater in an unheated garage.

There is little point in shutting off the lights in a heated room. Enjoy the light. You will be more cheerful when you pay the electric bill. Well, a little.