Since heat and temperature are both related to the same thing, the kinetic energy of the atoms in an object, how can we describe this relationship?

If heat is added to an object, its temperature will increase. If heat is taken away, its temperature will decrease. If an object has more mass, it will take more heat to raise its temperature the same amount than an object with less mass. These statements can be summarized mathematically by using a new physical constant, the specific heat capacity:

heat capacity =

How do I calculate Dsomething?

where q is the heat added or taken away in J, ΔT is the temperature change in ºC and m is the mass in grams. The specific heat capacity has units of J/gºC.

Different substances have different heat capacities. The table at right lists the specific heat capacities of some common substances.

Material

Specific Heat Capacity (J/gºC)

Al

0.902

C (graphite)

0.720

Fe

0.451

Cu

0.385

Au

0.128

NH_{3} (ammonia)

4.70

H_{2}O (l)

4.184

C_{2}H_{5}OH (l) (ethanol)

2.46

(CH_{2}OH)_{2} (l) (ethylene glycol, antifreeze)

2.42

H_{2}O (ice)

2.06

CCl_{4} (carbon tetrachloride)

0.861

CCl_{2}F_{2} (l) (a chlorofluorocarbon, CFC)

0.598

Wood

1.76

Concrete

0.88

Glass

0.84

Granite

0.79

Knowing about heat capacities allows you to answer questions relating heat and temperature. First, however, it is time to add two more steps to follow when working thermodynamics problems.

1. Define the system and surroundings.

2. Identify and assign signs to all the kinds of energy and work that enter or leave the system.

3. Predict the units your answer should have.

4. Predict the approximate size of your answer.

You can use these predictions to assess the accuracy of your answer when you are done.

Now compare your answer with the one below.

Please enter your answer in the space at left.

Because the water is changing temperature and is changing the most, it is the best choice for the system.

Step 2: Identify and assign signs to all the kinds of energy and work that enter or leave the system. Write your answer in the space below, then click on the Check button.

Now compare your answer with the one below.

Please enter your answer in the space at left.

Energy is entering the system in the form of heat. It has a positive sign. There is no other energy or work entering or leaving the system.

Step 3: Predict the units your answer should have. The question asks for an amount of heat, so the answer should be an amount of energy and have units of Joules.

Step 4: Predict the approximate size of your answer. Water has a very high heat capacity, about 4 J/gºC. Therefore the answer should be about 4 • 500 • 75=150,000 J.

What is the temperature change in the system? Click on the correct answer below.

What is the mass of the substance being heated? Enter the mass in the space below and click on the Check button.

Now compare your answer with the one below.

Please enter your answer in the space at left.

The mass is given as 500 g.

What is the heat capacity of the substance being heated? Enter your answer in the space below and click on the Check button.

Now compare your answer with the one below.

Please enter your answer in the space at left.

The heat capacity of liquid water is listed in the table above. It is 4.184 J / g ºC.

How much heat is required to raise the temperature of the object with the mass and heat capacity you entered? Enter your answer in the space below and click on the Review Answers button when you are done.

Correct! 157,000 J of heat are required to heat the water from 25 to 100 ºC.

While numerically correct, your answer has the wrong number of significant digits. Try again.

Remember to include the units with your answer.

That is incorrect. Please try again.

157,000 J of heat are required to heat the water from 25 to 100 ºC.