Help me understand the physics of electrical heaters and their efficiency

Question

I was having a conversation with my friend the other day. For a bit of background, I know next to nothing about physics, and he took physics lessons as part of his study to become an electrician before he changed his desired vocation.

I posed the idea that a PC is just as efficient as an electrical heater, and would produce an equal amount of heat if using the same amount of wattage. It was my logic that the electricity from a PC would ultimately end up as heat, and since energy can neither be created nor destroyed, so long as equal amounts of energy were being used, then the ultimate heat production would be identical.

He disagreed with me on this but ultimately said that he didn't know how to explain it in terms I would understand, as I did not have the background physics knowledge he had. So I was hoping someone here could clear it up for me.

My friend told me that heat is created when energy meets "resistance," and since electrical heaters are built to produce heat, the material they're made of would have better "resistance" for creating heat compared to a PC. So basically, the amount of energy in the room would be the same, but the amount of heat wouldn't.

Tangentially, something else he told me was that a heat source couldn't warm up its surroundings higher than its temperature. So if hypothetically, you had a perfectly isolated room with an electrical heater running at 60c and constantly producing heat by drawing power, the room would never go above 60c, regardless of how much wattage was being drawn into it over time. This also struck me as weird, because I can't imagine how you can keep pouring wattage into a room (that has no leakage) without it increasing the temperature. Although as I slept on it, I concluded that the premise of the question is wrong. Because heat won't move spontaneously from a colder place to a hotter place, the heater indeed won't be able to heat its surroundings to more than its temperature (because it won't have anywhere to dispense to if its surroundings are hotter), but doesn't that simply just mean that the heater itself will increase in temperature, then (assuming it has no temperature target feature and instead just keeps drawing in power)? So it'll initially run at 60c until the surrounding room reaches the same temperature, and then the heater itself will start to go above 60c, and the room temp will then rise along with it. That's the conclusion I came to, but I ultimately don't know if I'm right or not.

Answer 1

Usually when we speak of "efficiency" we refer to the proportion of the supplied energy that is not converted to heat. When heat is the desired end product this does not apply - as you correctly stated eventually all the supplied electrical energy gets converted to heat.

In this context it makes more sense to talk of efficiency in terms of how much of the supplied energy is used for the intended purpose. Usually the purpose of heating is to heat a room's occupants rather than large empty air spaces, and so the energy will be used more efficiently if the heaters direct hot air at the people in the room. In this sense a desktop computer will probably not be an efficient heater, as its heat is likely to spread though the room rather than warming you. A laptop may be different, assuming you want your lap warmed up. Some laptops have occasionally become hot enough to cause burns to the user's lap beneath them.

It is true that a heater cannot heat a room to be hotter than the heater's own temperature. Also the room cannot make the heater hotter than the room is. However the heater element is not heated by the room, but by the electricity passing through it, and it can easily get much hotter than the air in the room - consider a red hot bar radiator as an example. The heater element loses heat to the rest of the room, raising the temperature of the room to be a bit closer to the temperature of the element.

Answer 2

I know next to nothing about physics

Then we will use simple analogies to explain basic principle.

It was my logic that the electricity from a PC would ultimately end up as heat, and since energy can neither be created nor destroyed, so long as equal amounts of energy were being used, then the ultimate heat production would be identical.

So basically, the amount of energy in the room would be the same, but the amount of heat wouldn't.

Your intuition is correct. Most electricity is converted to heat during computer operation. A while ago when I had a crypto miner in my living room with rated power of about 1.5 kW, I did not have to use gas heating at all during winter. The miner was sufficient to heat up the place, I even had to cool down a little bit.

heat source couldn't warm up its surrounding higher than its own temperature.

Heat flows from a body at higher temperature to a body at lower temperature until their temperatures are equal.

So if, hypothetically, you had a perfectly isolated room with an electrical heater running at 60c and constantly producing heat by drawing power, the room would never go above 60c, regardless of how much wattage was being drawn into it over time. This also struck me as weird, because I can't imagine how you can keep pouring wattage into a room (that has no leakage) without it increasing the temperature.

In a perfectly isolated system, once heater and room reach 60 C no thermal power is needed to maintain that temperature. Let's use water tanks as an analogy to explain what exactly happens. Please note that this is oversimplification, but is good enough to understand basic principle.

In the figure below, (smaller) tank on the left is heater and (larger) tank on the right is room (air). The arrow indicates water volume flow that goes into the heater tank. These are analogies:

• water volume equals thermal energy (heat)
• water volume flow equals thermal power (volume over time; energy over time)
• water level equals temperature

Note that for the same water level (temperature), less volume of water (thermal energy) is needed for the heater tank than for the room tank. This corresponds to object's thermal capacity. Is it possible that water level is higher in heater tank than in room tank? It is, but two water levels naturally tend to equalize through the connection at the bottom - this is called heat transfer.

As long as you are pouring water into two tanks, the water level rises. This is a dynamic system, which means that while you are pouring water, the two water levels will not rise at the same rate, but they will equalize eventually! In reality the room tank has small holes through which water escapes to the environment - this is called thermal losses. Once desired water level (temperature) is achieved, in order to maintain the water level, the water volume flow (thermal power) must be equal to water volume flow that escapes to environment. And there is one general rule - the higher the water level is in the room tank, more water escapes in a unit of time.

^{Figure: Water tanks as an analogy to heat transfer between heater and room (air)}

Answer 3

I posed the idea that a PC is just as efficient as an electrical heater, and would produce an equal amount of heat if using the same amount of wattage.

While it is true that the total amount of energy being transferred will be the same, it may not be in the form of "heat", as discussed below. The bigger problem, however, is that the wattage of a PC is around seven to eight times less than an electric heater. That means a single PC would likely be inadequate to meet the requirements for raising the temperature of a room.

Basically, my friend told me that heat is created when energy meets "resistance," and since electrical heaters are built to produce heat, the material they're made of would have better "resistance" for creating heat compared to a PC.

I think what your friend is trying to say is that all or most of the electrical energy supplied to an electric heater is dissipated in electrical resistance. In the case of a radiant heater (having no fan) it would be 100%. In a PC some of the energy is use to generate sound and move air (fan).

So basically, the amount of energy in the room would be the same, but the amount of heat wouldn't.

First of all, the room does not "contain" heat. Nothing contains heat. Although you are new to physics, I'd like you to understand that heat is defined as energy transfer due solely to temperature difference. The proper term for the amount of energy contained by something (the air and materials of the room) is "internal energy", which is the sum of the molecular kinetic and potential energies of the molecules of the room. An increase in molecular kinetic energy results in the increase in temperature of the room.

Every watt of power consumed by both the PC and electric heater eventually increases the internal energy of the room by the same amount. But the way in in which they do it may be different. That's because there are two possible ways to transfer energy, heat and work. The components of the electric heater and PC whose temperature increases above the room temperature due to their electrical resistance transfers energy to the room by means of heat. The energy transfer due to sound and the movement of air by a fan are energy transfers by means of work, not heat.

The most important point insofar as raising the temperature of the air and materials in the room is the total amount of energy transferred to the room. In that respect, the PC would be inadequate.

Tangentially, something else he told me was that a heat source couldn't warm up its surrounding higher than its own temperature.

That is absolutely correct, and is more than a "tangential" point. As I already indicated, energy transfer by means of heat requires a temperature difference. Only those components and materials whose temperature is greater than the room temperature will transfer energy to the room in the form of heat since heat only occurs spontaneously (without work) from a higher temperature to a lower temperature.

...heat won't move spontaneously from a colder place to a hotter place, the heater indeed won't be able to heat up its surroundings to more than its own temperature

That's correct. But I can't imagine the temperature of the room equaling the temperature of the electric heater resistance elements. Ceramic elements of an infrared electric heater operate in the temperature range of 300-700 $^0$C

Hope this helps.

Answer 4

The main difference is the power required in each case. My desktop, linked to a flat screen TV gets 200 W, while the electrical furnace in the kitchen drags more than 1kW when turned on.

But you are right that at the end of the day, the watts consumed by the appliances result in heat transfer to the environment.

The room will not be warmer than the source of heat. But the temperature of this source on the other hand depends on the environment. The CPU cooler of the desktop can keep it in the design temperature range if the room is below $30^{\circ}C$ for example.

Answer 5

The question about heating a room and the temperature of the heat source is being looked at the wrong way. If you put power into a heater element it raises the temperature of the element, and the temperature of the element stops rising when the amount of heat going in (from electricity) is equal to the heat flowing out of the element (lets simplify it by assuming this is just by heating the air).

As the air temperature rises, so the loss of heat from the element at that temperature drops. But the same amount of heat is going into the element, so it will heat up to a higher temperature, until the heat loss is the same as the electrical power going in.

So say your room is at 10 DegC and the heater (your computer's mother-board) is at 60 degrees. By the time the air has warmed to 20 degrees, the board will be running at 70 deg.

Claudio mentions the CPU cooler of the desktop - that's a different matter, since that's a peltier cooler, so like a fridge it keeps the chip cool but pumps heat out into the room.