## Table of Contents

- What is Heat?
- Heat Capacity Definition
- Difference Between Heat Capacity, Specific Heat Capacity, and Molar Heat Capacity
- Heat Capacity Formula
- How to Calculate the Heat Capacity of a Substance
- Heat Capacity Examples
- Lesson Summary

See the heat capacity definition and symbol. View examples to learn how to use the heat capacity formula to calculate the heat capacity of a substance.
Updated: 08/13/2021

- What is Heat?
- Heat Capacity Definition
- Difference Between Heat Capacity, Specific Heat Capacity, and Molar Heat Capacity
- Heat Capacity Formula
- How to Calculate the Heat Capacity of a Substance
- Heat Capacity Examples
- Lesson Summary

Before investigating the concept of heat capacity, take a quick look at what heat is. **Heat** is a form of energy that is capable of flowing from one system to another. To understand heat as a transferable energy source, consider the boiling of water. When a vessel filled with water is placed on a burning stove, the bottom of the vessel first heats up, following which the water begins to get heated up until it finally starts boiling. This sequence of heat flow is directly related to the **temperature** of the vessel and the water; the temperature of a body is a measure of its hotness or coldness and it determines the direction of heat flow.

Thus, for heat energy to flow from one system to another, the two systems must have different temperatures. Heat will then flow from the hotter system to the colder system until the two systems reach the same temperature. Consider a bucket half filled with scorching hot water. To make the water slightly cooler, cold water is added to the bucket. Heat from the hot water makes the cold water warmer, until finally the mixture is at an intermediate temperature. Notably, it is the 'hotness' that flows among systems; 'coldness' is just the absence of heat.

As heat is a form of energy, it is measured in **Joules (J**) in the SI system and in **calories (cal)** in the CGS system.

{eq}1\:cal=4.184\:J {/eq}

In simple words, the **internal energy** of a system is the sum of the kinetic and potential energies of the molecules constituting the system. The molecules of a system exhibit random, chaotic motion, which results in the internal energy of the system. The internal energy of a system is closely related to its temperature. The more energetic the motion of the molecules, the higher is the internal energy of the system, and consequently, the higher is the corresponding temperature.

Now that the concepts of heat and internal energy have been defined, what is **heat capacity**? The heat capacity of a substance is the amount of heat energy required to raise its temperature by one unit. Heat capacity is thus an inherent property of a substance. For example, water has an extremely high heat capacity of 4184 J per kilogram. This implies that 4184 J of heat energy is needed to raise the temperature of water by 1 Kelvin (or 1 Celsius).

A very interesting effect that heat has on solid objects is the expansion of the dimensions of the object. This phenomenon is called **thermal expansion** and it can be of three kinds.

- Expansion of the length of the object or linear expansion
- Expansion of the area of the object or area expansion
- Expansion of the volume of the object or volume expansion

The heat capacity of a substance does not consider the amount of the substance. When the amount of the substance is also considered, the concepts of **specific heat capacity **and **molar heat capacity** are used.

The specific heat capacity of a substance is defined as the heat required to change the temperature of unit mass of the substance by one unit. The following expression is used to mathematically define the specific heat capacity.

Here, {eq}\Delta Q {/eq} is the amount of heat supplied, {eq}\Delta T {/eq} is the temperature change, and {eq}m {/eq} is the mass of the substance.

The SI unit of specific heat capacity is **Joules per kilogram per Kelvin** ({eq}Jkg^{-1}K^{-1} {/eq}.

Gaseous substances are usually expressed in terms of moles ({eq}\mu {/eq}) rather than mass. Thus, for gases, the molar heat capacity is generally used. Molar heat capacity is defined as the heat required to change the temperature of unit mole of the gaseous substance by one unit. It is given by:

The SI unit of molar heat capacity is **Joules per mole per Kelvin** ({eq}Jmol^{-1}K^{-1} {/eq}. Molar heat capacity can be defined at constant pressure ({eq}C_{p} {/eq}) or at constant volume of the gas ({eq}C_{v} {/eq}).

Consider the following table to understand the differences between heat capacity, specific heat capacity, and molar heat capacity.

Heat Capacity | Specific Heat Capacity | Molar Heat Capacity |
---|---|---|

1. It is the heat required for unit temperature change. | 1. It is the heat required per unit mass for unit temperature change. | 1. It is the heat required per mole for unit temperature change. |

2. It does not depend on the quantity of the substance. | 2. It depends on the mass of the substance. | 2. It depends on the number of moles of the substance. |

3. For example, water has a high heat capacity implies that a high amount of heat energy is required to raise the temperature of water by a certain degree. | 3. For example, the specific heat capacity of water is 4184 J/(kg.K) implies that 4184 J of heat energy is required to raise the temperature of 1 kg water by 1 K. | 3. For example, the molar heat capacity of water (at constant pressure) is 75 J/(mol.K) implies that 75 J of heat energy is required to raise the temperature of 1 mole of water by 1 K. |

In general, the specific heat capacity of substances is used to represent how much heat they require for changing their temperature. The table below provides the specific heat capacity values for some common substances.

Substance | Specific Heat Capacity in J/(kg.K) |
---|---|

Aluminium | 890 |

Copper | 385 |

Mercury | 140 |

Steel | 466 |

Water | 4186 |

When {eq}\Delta Q {/eq} amount of heat energy is supplied to a substance, resulting in a temperature change of {eq}\Delta T {/eq}, the heat capacity formula of the substance is given by:

Heat capacity is expressed in units of Joules per Kelvin ({eq}JK^{-1} {/eq}).

The above mathematical expression can be physically interpreted as follows.

High Heat Capacity Substance | Low Heat Capacity Substance |
---|---|

1. It requires high amount of heat energy for unit temperature change. | 1. It requires less heat energy for unit temperature change. |

2. It absorbs and releases substantial heat from and to the surroundings. | 2. It absorbs and releases lower heat from and to the surroundings. |

3. For example, water has a high heat capacity of 4184 J per kg. | 3. For example, mercury has a low heat capacity of 140 J per kg. |

The heat capacity equation is given by:

Here, {eq}\Delta Q {/eq} is the heat supplied to the substance and {eq}\Delta T {/eq} is the corresponding change in temperature.

Consider a substance at a temperature {eq}T_{1}\:K {/eq}. When {eq}X\:J {/eq} of heat is supplied to the substance, its temperature increases to reach a final value of {eq}T_{2}\:K {/eq}. To calculate the heat capacity of the substance, consider the following steps.

- The heat supplied is given. So, {eq}\Delta Q=X\:J {/eq}.

- The change in temperature, {eq}\Delta T=T_{2}-T_{1} {/eq}.

- Thus, the heat capacity, {eq}S=\frac{\Delta Q}{\Delta T}=\frac{X}{T_{2}-T_{1}}\: JK^{-1} {/eq}.

Consider the following examples of heat capacity calculation.

When {eq}2\:kJ {/eq} heat is supplied to a copper block, its temperature changes from {eq}15\:K {/eq} to {eq}9.8\:K {/eq}. Calculate the heat capacity of the block.

Here, {eq}\Delta Q=2000\:J {/eq} and {eq}\Delta T=15-9.8=5.2\:K {/eq}

Thus, the heat capacity

What amount of heat energy is required to raise the temperature of water by {eq}10\: ^{\circ}\mathrm{C} {/eq}?

Given, {eq}\Delta T=10\: K {/eq} (as unit change of temperature is the same in {eq}^{\circ}\mathrm{C} {/eq} and {eq}K {/eq})

We know that heat capacity of water {eq}S=4184\:JK^{-1} {/eq}.

Now:

An aluminium slab at {eq}293\:K {/eq} is supplied with {eq}5\:kJ {/eq} of heat. What is the final temperature of the slab?

We have,

Here, {eq}\Delta Q=5000\:kJ {/eq}, {eq}S=890\:JK^{-1} {/eq}, and {eq}T_{1}=293\:K {/eq}. Substituting these values in the above equation, we get the final temperature as:

**Heat** is a form of energy that flows from one system to another. The direction of heat flow depends on the **temperature** of the concerned systems; heat always flows from the hotter body to the colder body. The **internal energy** of a system is the total energy of the system's constituting molecules and it manifests as the temperature of the system.

Heat supplied to a body can be related to the corresponding rise in temperature. The amount of heat required to raise the temperature of a substance by one unit is called the **heat capacity** of the substance. Inclusion of the mass and the mole of the substance to the definition of heat capacity corresponds to the **specific heat capacity** and the **molar heat capacity**, respectively.

The heat capacity equation is given by:

{eq}\Delta Q {/eq} is the heat supplied for the temperature change of {eq}\Delta T {/eq}.

The heat capacity is expressed in {eq}JK^{-1} {/eq}.

A substance with high heat capacity is capable of absorbing a high amount of heat from its surroundings, whereas a substance with low heat capacity can only absorb a small amount of heat.

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- Activities
- FAQs

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**

- True
- False, because the correct statement is,
*Water has a much higher capacity for storing heat energy than sand*. - True
- 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*. - False, because the correct statement is,
*Heat energy is transferred from a body of higher temperature to those with a lower temperature*. - True
- True
- True
- 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.*. - False, because the correct statement is,
*In the International System of Units, Joule is the derived unit of energy, work, and heat*.

In thermodynamics, the heat capacity is a measure of the heat required by a substance to raise its temperature by a specific degree. The heat capacity is defined as the amount of heat that is needed for a unit rise in the temperature of the substance.

The heat capacity of a substance (S) is equal to the ratio of the amount of heat energy supplied to the substance (Delta Q) to the corresponding rise in temperature (Delta T).

S=Delta Q/Delta T

The heat capacity is determined by the quantity of heat energy supplied to the concerned substance. It is also dependent on the initial and final temperatures of the substance.

The heat capacity of a substance is the ratio between the heat supplied to the substance and the corresponding temperature change. Thus, the SI unit of heat capacity is Joules per Kelvin (J/K).

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