Heat capacity and specific heat

Understanding how substances absorb and store thermal energy is important in thermodynamics, a fundamental part of chemistry and physics. Two essential concepts that describe these processes are heat capacity and specific heat. In this comprehensive explanation, we will understand these concepts in an accessible way and provide plenty of examples to illustrate their applications.

What is heat capacity?

Heat capacity is the amount of heat energy needed to change the temperature of an object or substance by a certain amount. It is an extensive property, meaning it depends on the amount of matter or the size of the object. This means that larger objects or amounts of matter have a greater heat capacity because there is more space to heat them.

The formula for heat capacity (C) is:

C = Q / ΔT

Where:

• Q is the heat added (in joules or kilocalories).
• ΔT is the temperature change (in Celsius or Kelvin).

For example, consider heating a large pot of water on the stove. The pot has a high heat capacity because a fair amount of energy is required to raise its temperature. If you pour some water from the pot into a smaller pan and heat that, the water in the smaller pan will heat up much faster than it would in the pot because it has a lower heat capacity.

What is specific heat?

Specific heat is a more intrinsic property, referring to the amount of heat needed to change the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). It is an intensive property, meaning it does not depend on the amount of substance or the size of the system. By comparison, specific heat is a more useful value for chemists and physicists because it describes the material rather than the quantity of the material.

The formula for specific heat (c) is:

c = Q / (m * ΔT)

Where:

• Q is the heat energy supplied (in joules).
• m is the mass of the substance (in kilograms or grams).
• ΔT is the temperature change (in Celsius or Kelvin).

Specific heat helps to compare how different substances react to the same heat input. For example, the specific heat of water is about 4.18 J/g°C. This means that you need 4.18 J of energy to raise the temperature of one gram of water by one degree Celsius. This is relatively high compared to metals such as iron, which have a lower specific heat value.

Comparison of heat capacity and specific heat

While both heat capacity and specific heat describe an object or substance's response to heat energy, they have important differences due to their dependence on mass. Heat capacity is more concerned with the total amount of heat a system can absorb, while specific heat focuses on how a particular type of material behaves when receiving heat.

Here's a practical example to make this clearer: imagine a glass of water and a swimming pool. While the pool has a much higher heat capacity than the glass of water because it contains so much more water, the specific heat of the water in the glass is the same as the specific heat of the water in the pool. Both require the same amount of energy per unit mass to change the temperature by one degree, which highlights how the specific heat is independent of the size of the system.

Examples and applications

Example 1: Calculation of heat absorbed by water

Suppose you have a 100-gram sample of water, and you want to calculate the heat absorbed as its temperature rises from 25°C to 75°C. Given that the specific heat of water is 4.18 joules/gram°C, you can use the formula for specific heat to find the answer:

Q = m * c * ΔT
Q = 100g * 4.18 J/g°C * (75°C - 25°C)
Q = 100g * 4.18 J/g°C * 50°C
Q = 20900 J

Water absorbs 20900 joules of heat energy.

Example 2: Understanding different materials

Consider two different materials: aluminum and copper. The specific heat of aluminum is about 0.897 J/g°C, and copper is about 0.385 J/g°C. Suppose you have 150 grams of each, and both start at the same initial temperature. If you add the same amount of heat energy to each, the temperature of copper will rise more because it has a lower specific heat.

This principle is why materials such as copper and aluminium are often chosen for use in cooking vessels and heat exchangers; they heat up quickly and transfer heat energy efficiently.

Visual example

Example 3: Cooling and heating curves

It can also be very illustrative to visualize how the temperature of substances changes. When a substance is heated or cooled, it can go through different phases, each of which has a different heat capacity.

This temperature curve shows how a common substance might behave when heat is applied. Initially, when the substance is in the solid state, its temperature rises steadily. When the solid melts and changes to a liquid, the temperature becomes constant, even though heat is still being added. This is because energy is used to change states rather than to increase the temperature. This process also occurs during boiling, where the temperature remains constant while the liquid turns to a gas.

The specific heat and heat capacity will vary during each stage and transition, because each stage requires a different amount of energy to change the temperature or state.

Further applications: Earth's climate

Heat capacity and specific heat have important implications beyond personal or laboratory-scale applications. An important example of this is the Earth's climate system. Large water bodies such as the oceans have a high heat capacity. They absorb a substantial amount of solar energy without undergoing large temperature changes, which helps moderate the climate and plays an important role in weather and climate patterns.

Because the specific heat of water is greater than that of land, coastal areas typically experience milder climates than inland locations where temperature fluctuations are greater. In summer, oceans absorb and store heat, causing temperatures to rise. In winter, they release the stored heat, causing temperatures to drop.

Conclusion

The concepts of heat capacity and specific heat are fundamental to understanding how substances interact with thermal energy. By investigating these properties, scientists and engineers can design better systems for heating, cooling, and transferring energy. Whether in everyday devices, industrial systems, or natural phenomena, these principles provide a basis for predicting and optimizing thermal interactions in our world.

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