I am trying to calculate the energy needed to heat 1 gal of water from x to y degree so I can find the cost?

Question

I knoe the cost per therm of gas which is needed to heat the water. 1) form x to y degree, and 2) from x to boil for staem. The volume of water heated is different, it could be 500 gallons, or less or more. The temps normally is 75 to 180, and 75 to staem. Please provide the method of how this is done for future calcs.

Thanks

Answer 1

energy required is directly proportional to water volume, e.g. to heat 10 gallons of water from X degrees to Y degrees would take 10x the energy to heat 1 gallon by the same temp difference.

temperature differential is also directly proportional, e.g. to heat X gallons 20 degrees takes 2 times the energy to heat X gallons by 10 degrees.

for a formula based on your question the energy to heat a specific number of gallons by a specific temperature would be

energy to heat 1 gallon x gallons to be heated x temp difference/(temp Y - temp X)

Answer 2

Some people are using the Imperial system .. nothing wrong with that.

Sensible heat: Heating water = 1 Btu/lb/°F. (Up to 212°F)
Latent Heat: Vaporising water = 144 Btu/lb/°F (At 212°F)

1...Gals x ΔT x 10 Btu = Temp. change °F.

2... Gals x 10 x 144 Btu = Vaporisation of water)

(The same figures are used for condensing, cooling and freezing. (Releasing heat energy)

The cost per therm is dependent upon the number of Cubic Feet of gas used.
Your gas bill will give you the conversion details.

(I believe the US system of gallons is a little different).

.....

Answer 3

Just use this formula:

Energy = m x c x (T2 - T1)
(T2 - T1) is change in temperature in kelvin but it does not matter if you use Celsius provided you are consistent;

Mass of water will be same as volume of water i.e. for 1 gal = 4.5 litres = 4.5 kilos roughly!!

c = 4200 joules

For example, 1.5 kg of water at 15 deg c is boiled. Energy required is:

E = 1.5 x 4200 x (100 - 15) = 5.4 x 10^5 J

Hope this helps

Answer 4

You haven't provided enough information...

A therm of gas AS USED BY THE GAS COMPANY to charge for gas is 100 cubic feet of natural gas. This is a unit of VOLUME not a unit of energy.

You know how much one therm of gas costs but, depending on the efficiency of your stove (or furnace) you don't know how hot it burns.

The value of a therm for physics is different and it varies depending on whether it is a UK therm (105,505,585.257 348 joules ), an EU therm (105,506,000 joules) or a US therm (105,480,400 joules.)

Depending on the water's container, it will take various amounts of heat to warm the water due to the heat transfer rate of whatever material the container is made of. i.e.; A copper pot will require a different amount of heat than a stainless steel or cast iron pot. The size and thickness of the pot will make a difference too!

As will the distance between the bottom of the pot and the flame. (The air will dissipate the heat, especially if there is a draft in your kitchen!)
;->
.

Answer 5

Me, I would organize the thoughts better. Convert from English units to SI, then use the fact that it takes 1 calorie to raise 1 cc of water 1 degree centigrade. If you are converting to steam, don't forget the latent heat of vaporization. 500 Gallons is a lot of water and will require a great deal of heat

Answer 6

I see we are all being asked to do your physics homework. One question OK. Four or five that you really should have listened to in class or looked up in a textbook is too much. Google your questions on the net and work it out for yourself.