240volts vs 208volts

[captron5677]

Here's a question that I came across the other day. What do you think?
I've got a heater rated at 2000watts at 208volts.What would it's rating be at 240 volts.
Till Later Ron

 

[ronaldrc]

Re: 240volts vs 208volts

2000 x 1.154=2308 watts at 240 volts

Ronald

 

[sirdle]

Re: 240volts vs 208volts

Are you sure that's right?

It seems to me that the thing which is constant in the two cases is the internal resistance of the heater. Changing the voltage will also change the current. So we need to use a form of the power equation which uses only resistance and voltage. Suppose we use uppercase letters for 240v and lower case for 208v (I assume this is a single phase installation?).

Then P = (E x E)/R and p = (e x e)/r, but R = r. So if we divide the first equation by the second the R and r cancel out. If we multiply both sides of the equation by p, we get P = p x (E x E )/(e x e). So when we put numbers in we get P(at 240v) = 2000w x (240v x 240v)/(208v x 208v). So the power at 240V would be 2663w.

Did I miss something here?

 

[luke warmwater]

Re: 240volts vs 208volts

Using Ohms Law:

R=E^2/P P=E^2/R

R=208x208/2000 P=240x240/21.63

R=21.63 P=2663

If this is a test question, I find it more often to be asked the other way around.
Example:
single phase, 240volt 5500watt water heater is connected to a 208volt system. What is the connected wattage and full load current?

 

[ronaldrc]

Re: 240volts vs 208volts

You're right Sirdle it would be around 2,662 watts. I didn't even check my figures to see if they where right.

Normally I would have found the resistance with ohms law then then used 240 to find my power but I thought I had an other way figured out from the old Org. post but not so.

Ronald

 

[captron5677]

Re: 240volts vs 208volts

Hey Guys, Ok well the math is right,but the question asks what the new RATING of the heater would be.

 

[rattus]

Re: 240volts vs 208volts

Gents, let me remind you that the temperature coefficient of nichrome is significant, therefore you cannot assume constant resistance. The power would not go as high as you predict. And, unless the heater is rated for 240V, I would be concerned that the heating element would fail prematurely, and it might get hot enough to open the safety fuse. Furthermore, if it uses a fan to move the heat, the heating element would not run as hot, and this would further complicate the matter.

 

[don_resqcapt19]

Re: 240volts vs 208volts

The supply voltage has nothing to do with the rating of the heater. Yes, its output will change with a change in the voltage, but that will not change the numbers on the nameplate. The rating is whatever is marked on the nameplate.
Don

 

[sirdle]

Re: 240volts vs 208volts

I always have trouble with the concept of "rating." It is not defined in article 100. Does anyone have a good definition?

My copy of Webster's defines it as: "The designated operating limit for a machine based on specified conditions." This would seem to imply that the heater is not rated (Edit --- at the new voltage), unless the nameplate indicates otherwise. Is this right?

[ April 23, 2005, 01:03 PM: Message edited by: sirdle ]

 

[rattus]

Re: 240volts vs 208volts

Originally posted by don_resqcapt19:
The supply voltage has nothing to do with the rating of the heater. Yes, its output will change with a change in the voltage, but that will not change the numbers on the nameplate. The rating is whatever is marked on the nameplate.
Don

I beg to differ. The voltage rating is part of the overall rating. That is, this heater produces 2KW of heat when 208V is applied. Likewise, a 100W lamp produces 100W, mostly heat, when 120V is applied. In either case, exceeding these ratings tends to shorten the life of the heating element or filament. Doubling the voltage would result in instant failure.

Resistor power ratings indicate only the maximum allowable dissipation, e.g., a 1-watt resistor can safely dissipate 1 watt under standard conditions. Designers however usually build in a safety factor plus derating for ambient temperatures above standard conditions.

Resistor voltage ratings are not tied to the power ratings as they are in lamps and heaters.

[ April 23, 2005, 12:56 PM: Message edited by: rattus ]

 

[don_resqcapt19]

Re: 240volts vs 208volts

rattus,
This is not a resistor. It it a piece of equipment that has a rating established by the manufacturer and the listing agency. Connecting this equipment to a different voltage does not change the equipment rating. Sure it changes the operation and heat output, but the rating has not changed and can only be changed by the manufacturer and the listing agency. Misuse of the equipment in the field does not change its rating.
Don

 

[rattus]

Re: 240volts vs 208volts

Don, of course. I was merely drawing a comparison between the two items.

In short, I am saying that the voltage and power ratings of an electric heater are intimately connected which is not true of an off the shelf resistor.

When you apply rated voltage to a heater you get rated power. If you apply rated voltage across a resistor, you may fry the resistor.

 

[john m. caloggero]

Re: 240volts vs 208volts

First of all it is a violation of 110.3(B).
Assuming that the temperature rise is linear for the heating element (which it is not), but for the sake of a basic calculation, Watts actual = (actual v/ rated V) sqaured x rated heater watts.
((240/2080^2)x rated watts = 1.33 x 2000 = 2663W.
Certainly the heater element will be shortened and the temperature rise of adjacent materials may be ignited due to the elevated temperature. Don't do it!!

 

[edavis2293]

Re: 240volts vs 208volts

This question was on my Masters exams in Washington, City of Houston, and Alaska. Theoretically the power varies by the square of the voltage, therefore,

240/208=1.15

1.15 squared = 1.331

1.331 x 2000 = 2663 w

Summary is: don't do it for the reasons given by John Caloggero.

 

[rattus]

Re: 240volts vs 208volts

Did anyone notice that

240/208 = 1.15

is the O.F.F., the infamous Oregon Fudge Factor?

 

[charlie b]

Re: 240volts vs 208volts

Let's not go there!

The answer that the author of the test question would grade as "correct" would probably be 2662. The "true answer," the "real world what do you do if a customer wants you to install it answer," is, as several have said before, "The rating is whatever the manufacturer says the rating is." If the manufacturer does not give it a 240 volt rating, then it would be a violation to install it on a 240 volt source, as John has pointed out.

 

[steve66]

Re: 240volts vs 208volts

Heating elements and heaters are often dual rated, and the theoretical formula of using the square of the voltage ratio's often gives a very accurate answer. For example, I just used a single phase duct heater rated 10KW at 240v, and 7.5 kw at 208 volts.

Rattus: If a fan is present, that helps the heater maintain about the same temperature for both voltages. So it doesn't complicate the matter, it simplifies it. Again, the result is that the theoretical formula is very close to what you would get in reality.

Steve

 

[rattus]

Re: 240volts vs 208volts

Steve, you are right in your claim that a fan would tend to stabilize the temperature, but it adds another variable to the problem.

Now for a surprise: The TC of nichrome is 0.0004 per Centigrade degree--one tenth that of copper! Of course, a heater is expected to operate at a red hot temperature but copper wire is not.

Now who knows the temperature of a a red hot or white hot heating element? From that we could make some rough calculations.