If you wanted to warm 100 kg of water by 20 degrees Celsius for your
bath, how much heat is required?  (Calories, Joules)

Hi!!


The specific heat is the amount of heat per unit mass required to
raise the temperature by one degree Celsius at constant atmospheric
pressure.
The specific heat of water is 1 calorie/gram*°C = 4.186 joule/gram*°C 
i.e., 1 calorie is needed per degree Celsius (or Kelvin) of
temperature change for 1 gram of liquid water.

Q = c * m * (Tf - T0)

where:
Q = change in heat energy or heat added to the sample (if negative
heat substracted);
c = specific heat;
m = mass of the sample;
(Tf - T0) = final temp less initial temp = change in temperature of sample .

Note that the above formula does not apply if a phase change is
encountered, because the heat added or removed during a phase change
does not change the temperature.

Now the problem:
We have 100 kg of water, so we have 100,000 grams of water, and we
want to raise its temperature 20ºC:

Q = unknown;
c = 1 cal/g*°C = 4.186 joule/g*°C ;
m = 100,000 g ;
(Tf - T0) = 20ºC

Then:
Q = 1 cal/g*°C * 100,000 g * 20ºC =
  = 2,000,000 calories

Q = 4.186 joule/g*°C * 100,000 g * 20ºC =
  = 8,372,000 joules

The required heat is 2,000,000 calories or 8,372,000 joules.


I hope that this helps you.

Regards.
livioflores-ga

Your answer relates to the specific heat of a substance, in this case
water.  This is the amount of energy required to produce a 1°C
temperature change per unit of mass.

* For water, you need about 4184 joules to raise the temperature of 1 kg water 1°C.
* Also, 1 calorie of heat is required to raise temperature of one gram of
water by 1 degree Celsius. 1 calorie is 4.184 joules


So, if you had 100kg of water and wanted to raise it 20 deg C.  Your
looking at about 100kg*20deg*4184 = 8,368,000 Joules.




Hope this helps.
Jesse

Calories, written with a big C, usually means kilocalories, (that's
the kind of Calories used to measure the energy content of food) so in
this unit, the answer is 2000 Calories (which is about 1 day's worth
of food).