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Heat Capacity: Definition & Equation

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Amy Lange

Amy has taught university-level earth science courses and has a PhD in Geology.

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Christianlly Cena

Christianlly has taught college Physics, Natural science, Earth science, and facilitated laboratory courses. He has a master's degree in Physics and is currently pursuing his doctorate degree.

Heat capacity is the ratio between the rise in temperature of an object and the amount of energy transferred to the object. Study the definition and equation of heat capacity, understanding heat, and the specific heat of an object. Updated: 11/02/2021

What Is Heat Capacity?

Have you ever gone to the beach and noticed the sand is extremely cool in the morning and hot in the afternoon, while the temperature of the water doesn't seem to change at all? Both are subjected to the same amount of energy from the sun, but the different properties of water and sand cause them to react differently. One of the reasons for this phenomenon is that water has a much higher heat capacity than the sand, which simply means that it takes much more energy to raise the temperature of water than it does for sand.

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  • 0:00 What Is Heat Capacity?
  • 0:35 Understanding Heat
  • 1:35 Defining Heat Capacity
  • 3:05 Specific Heat
  • 3:45 Lesson Summary
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Understanding Heat

To understand heat capacity, we must first understand heat. When we talk about heat, we're often referring to whether an object feels hot or cold. This is because heat is actually a form of energy that flows from objects of higher temperature to those with lower temperature. So if I touch a hot coffee mug, the mug will feel hot because the energy from the mug is being transferred to my cooler hand. Similarly, if I pick up a glass of ice water, the heat from my hand is flowing into the glass, making the glass feel cold.

Internal energy is the sum of kinetic and passive energy within an object compared to an object at rest. We already know that heat refers to the transfer of energy due to a temperature difference between objects. Thus, an object can contain internal energy but it cannot contain heat. Since heat is a form of energy, the SI unit for heat is the joule (J). Heat is commonly noted as Q in equations.

Defining Heat Capacity

Heat capacity (C) is the amount of energy needed to raise the temperature of a specific substance by 1 degree Celsius. Heat capacity can also be viewed as the ratio of the amount of energy transferred to an object and the resultant temperature rise (deltaT).

C = Q / deltaT

The heat capacity units are J / degree Celsius. Because the heat capacity of an object is dependent on the mass of the object, heat capacities are often given per 100 grams to allow for a comparison between objects of equal mass.

Let's revisit our example of the temperature of the water and sand at the beach. We'll assume that the heat capacity of water is 400 J / degree Celsius and the specific heat of sand is 80 J / degree Celsius. Let's calculate how much heat (Q) is required to raise the temperature of the sand and water by 5 degrees Celsius.

Since we're interested in Q, we must first rearrange the equation.

For water:

Q = 400 J / degree Celsius x 5 degrees Celsius = 2000 J

For sand:

Q = 80 J / degree Celsius x 5 degrees Celsius = 400 J

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Additional Activities

Heat Capacity True or False Activity

Directions

Determine whether the following statements are true or false. To do this, print or copy this page on a blank paper and underline or encircle the answer.

1. Specific heat denotes the amount of heat required to raise the temperature of a substance per unit of mass.

True | False

2. Sand has a much higher capacity for storing heat energy than water.

True | False

3. Internal energy is defined as the energy associated with the random, disordered motion of molecules within an object.

True | False

4. The amount of heat required to change the temperature of water (with a heat capacity of 400 Joules/degree Celsius) by 30 degrees Celsius is 1200 Joules.

True | False

5. Heat energy is transferred from a body of lower temperature to those with a higher temperature

True | False

6. In the same sunlight, the temperature of water increases more slowly than the temperature of the sand.

True | False

7. Different substances have different capacities for storing heat energy.

True | False

8. The amount of heat, Q, is directly proportional to mass and resultant temperature.

True | False

9. Heat capacity is defined as the amount of energy required to increase the temperature of a specific substance by 10 degrees Celsius.

True | False

10. In the International System of Units, Celsius is the derived unit of energy, work, and heat.

True | False


Answer Key

  1. True
  2. False, because the correct statement is, Water has a much higher capacity for storing heat energy than sand.
  3. True
  4. False, because the correct statement is, The amount of heat required to change the temperature of water (with a heat capacity of 400 J / degree Celsius) by 30 degrees Celsius is 12000 Joules.
  5. False, because the correct statement is, Heat energy is transferred from a body of higher temperature to those with a lower temperature.
  6. True
  7. True
  8. True
  9. False, because the correct statement is, Heat capacity is defined as the amount of energy required to increase the temperature of a specific substance by 1 degree Celsius..
  10. False, because the correct statement is, In the International System of Units, Joule is the derived unit of energy, work, and heat.

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