Looking to heat a ceramic cup

Although V*I=P, it also heavily depends on the way you are going to do this.

The temperature of the wire itself is easily calculated with fore mentioned formula and some table for that material but the heat transfer to the cup is a different matter. On top of that you will have loss so again you should add to the found figures.

Maybe you should elaborate more so we have a fighting chance or do a trial and error experiment.

I will be adding a heat transference cement to the wire to transfer the heat to the outside of the cup. Should we say a 10% heat loss from the cement to the inside of the cup.

You'd need to know the heat loss from the cup to be able to figure the heat input required to maintain a temperature. If the cup is empty, then some of the heat will be lost through radiation from inside and out, some will be lost to conduction (assisted by convection) to surrounding air. I'd guess that you must want to have something in the cup, however, rather than using the cup simply to give people burns and to melt holes through your dashboard. If whatever is in the cup vaporises, then much of the heat input will go to changing the phase of the material in the cup.

If I were to make a guess, 60 watts (5 amps at 12 volts) would would bring an empty coffee mug to about the temperature you want, and hold it there in an environment of around room temperature. This is pure gut-level guess, and to get closer you'd need to figure the radiation of the cup, conductance, vaporization, etc.

Probably just as easy to simply buy some nichrome, wrap is around the cup (10 turns or so) and try it. Many multimeters are overload protected, so if you used the 10 amp scale and found you were overloaded, then you'd want to use a longer piece of nichrome. If your multimeter lacks overload protection, then don't use it -- you could wreck the meter.

BTW, for temperatures like this, stainless steel safety wire works well too for experimenting. I use SS wire for cutting plastic foam, with a small battery charger for the supply.

Careful not to get burned: the element anywhere not firmly in contact with the cup will be very hot -- and the cup itself, at 300 degrees, would cause second degree burns too.

12 V X 15A = 180 Watts.

This seems very low to get anything heated up to 300Deg F which is 149 Deg C. Consider that boiling point of water is around 100 Deg C so you are wanting to go beyond that. I reckon you cannot do this with only 180 Watts as you will have too large a loss to achieve that temperature in the first place. You have elaborated only very little on your project bit I guess this is because you are actually very uncertain about this whole thing yourself. Cups normally have open tops so you loose a lot there as well. What material is the cup and what is in it, i.e what are you heating up insiude.

You say heat transfer cement but that is an oxymoron. You either mean heat transfer paste, to go between the surface of the cup and your heater, or cement which is just heat resistant cement or putty. Again it only shows you are not familiar with what you are asking here.

Please take my advise and go do some experiment, you cannot do much damage with this setup as long as you make sure you fuse the cigarette lighter properly. I think you will find that you cannot achieve your set temperature, let alone hold it. Remeber that most household kettles are 1.5 or 2 Kwatt. The time it takes to boil a cup load of water is still between 5 or 10 minutes or so. You are trying to do this with only 180 Watt. ???

You're such a wet blanket!

This hot cup is only 24 watts.

This one is only 12 watts.

This one is 15 watts.

Some insulation on the sides and top, and you'd be all ready for those impromptu fondue parties. Or how about a hot cheese dip for french fries?

The filament of a 2 watt light bulb operates at about 1800 C so all we need is plenty of insulation to keep the fondue hot (until we take off the lid.)

They make little heaters that you stick in your cup to bring it to a boil. One of the main reasons to use ceramic cups is that the inside can be 190°F (absolute maximum for coffee before it goes bitter) and you can still hold the outside. If you reverse the process, only the outside will ever get to 300°F since the inside will always be cooled by the latent heat of vaporization of the water in there. Unless, of course, you have an empty cup but then why heat it?

As a hand-waving argument, taking this heatsink as a model for your cup (it's 2.3°C/W), you should be able to reach your temperature. The lowest resistance you can go to for 12V @ 15A is 0.8Ω. Find some wire (about 0.05 - 0.1 Ω/ft ()) and try it.

I'd suggest fitting an in-line fuse, ensuring good thermal conductivity all over, and doing first experiments with cup+heater in a bucket of water.

[Note for other would-be DIY-ers: don't do this with a mains-powered heater !!!]

One reason you have not received a convenient answer is because you have not provided enough information. You need to tell us how fast you want the coffee cup and its contents to reach the desired temperature, and whether you will provide a shut-off when that temperature is reached, or whether the contents should continue to get hotter.

Further information requested. The ceramic mug will have silicone oil inside. The cup will have a lid. I am looking to maintain the temperature of the silicone oil at 300 degrees F continuously. I would like to bring the temp. up within 5 to 7 minutes and maintain. So I will probably need a thermostat.

The wire will be coated with Saurisen Thermoconducting Cement and wrapped with insulation to prevent the heat from escaping away from the cup.

Now, what resistance in the nichrome wire, the length of the wire, and the cross area of the wire would I use to complete the desired operation using the power available from a car cigarette lighter? 12 volts X 10 amps.

You can follow this link for a table http://www.wiretron.com/nicrdat.html

Thank you for your help. I'll see where this goes.

You could make a coil of nichrome and bond that to the bottom of the cup with the cement. If we assume 12 amps while the coil is at room temp (the temperature rise will increase the resistance when the coil is at operating temp) then your coil should be 1 ohm. Per the chart here, 19 gauge is .5 ohm per foot, so a 2' coil would be 1 ohm. For the temperatures you are interested in, the change in resistance with temperature is not great.

Silicone has a high boiling point, so the energy input will mainly be used simply to raise the fluid's temp.

(120 watts) x 300 seconds = 8 604.2065 calories, per google calculator, so you could raise the temp of 100 cc of water by 86 C in five miuntes. However, per this site, silicone requires only .37 cal/g/degC (and the density of most silicone fluids is less than that of water) so you'd be fine, even allowing for losses to the environment.

If you were taking the lid off frequently, or removing fluid and replacing it with cool fluid, then you'd have to figure in the additional heat loss.

If you are going to use this to cook french fries while driving, I'd recommend vegetable oil, instead of silicone.

BTW, make sure your coils do not touch -- you might want to arrange the wire in zig-zag fashion, to avoid having wires crossing.

Thank you for your help. I will try your suggestions and see what happens.

I think you now have enough information to round off to the nearest right answer. Only one additional caution. Don't have the cup in your lap when you first turn this thing on. Hot wires attached to the cup surface will create thermal shock, which the cup won't appreciate. It may fracture.