# Heat Capacity: Definition & Equation

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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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Lesson Transcript
Instructor: Amy Lange

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

This lesson covers the topic of heat capacity, which is a core concept of thermodynamics. We will review the definition of heat and explore how it relates to an object's heat capacity.

## 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.

## 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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