Counting calories Back to main heat and temperature page
calorie: 1 calorie will raise 1 gram of water 1 degree Celsius. If 1 g of water is given 2 calories, its temperature will go up 2 degrees. 

Melting ice at 0 degrees Celsius: It takes 80 calories to melt 1 gram of ice. If 1 g of ice (at 0 degrees Celsius) is given 80 calories, it will melt and the final temperature of the water will be 0. 

Freezing water at 0 degrees Celsius: It also takes 80 calories to freeze 1 gram of water. If 1 g of water (at 0 degrees Celsius) gives away 80 calories, it will freeze and its final temperature will be 0. 

Boiling water at 100 degrees Celsius: 540 calories are needed to turn 1 gram (at 100 degrees Celsius) of water to steam. 
Problems dealing with changing the temperature of water.
Example 1) Pretend that you have 10 grams of water at 70 degrees Celsius. How many calories are needed to get the sample to boiling? (Boiling occurs at 100 degrees Celsius)
Heat 
= 
Mass 
X 
(F 
 S) 


= 
10 
X 
(100 
 70) 


= 
10 
X 
30 



= 
300 
calories 

Example 2) You have 200 grams of water at 65 degrees Celsius. If you apply 2000 calories to the sample, what will the final temperature be? Plug the number under the equation to solve.
Heat 
= 
Mass 
X 
(F 
 S) 
2000 
= 
200 
X 
(F 
 65) 
Divide both sides of the equation by 200
10 
= 
F 
65 
+65 


+65 
F = 75 degrees Celsius
Problems dealing with changing phase from ice to water.
Example 1) 110 calories are given to 1 gram of ice. What is the final temperature of the water?
Heat 
= 
Mass 
X 
(F 
 S) 
30 
= 
1 
X 
(F 
 0) 
30 
= 
1 
X 
F 

F= 30 Degrees Celsius
Example 2) 10,000 calories are given to 100 grams of ice. What will the final temperature of the water be?
Heat 
= 
Mass 
X 
(F 
 S) 
2000 
= 
100 
X 
(F 
 0) 
2000 
= 
100 
X 
F 

F= 20 Degrees Celsius
Problems dealing with changing phase from water to steam.
Example 1) 2000 calories are added to water at 100 degrees Celsius. How many grams of water will be boiled away?
Example 2) 100 grams of water at 70 degrees Celsius receive 4000 calories. How many grams of water will be boiled away?
Heat 
= 
Mass 
X 
(F 
 S) 

= 
100 
X 
(100 
 70) 

= 
100 
X 
30 


= 
3000 
calories 

