Problem 21 - An Introduction to Thermal Physics

Question

Is heat capacity \((C)\) extensive or intensive? What about specific heat \((c) ?\) Explain briefly.

Step-by-Step Solution

Answer

Heat capacity \(C\) is extensive; specific heat \(c\) is intensive.

Step 1: Understanding Heat Capacity and Extensivity

Heat capacity, denoted as \(C\), is defined as the amount of heat required to change the temperature of a given body by a certain amount. An extensive property depends on the amount of substance present. Since heat capacity scales with the size or quantity of the material, \(C\) is an extensive property.

Step 2: Understanding Specific Heat and Intensivity

Specific heat, denoted as \(c\), is defined as the heat capacity per unit mass of a substance. It does not change with the amount or size of the sample. As such, \(c\) is an intensive property because it remains constant regardless of how much material is present.

Key Concepts

Heat Capacity

Heat capacity is a measure of how much heat energy a substance can absorb before it experiences a temperature change. Imagine you're heating up a large pot of water on the stove. The energy needed to increase the temperature of all that water is the heat capacity of the pot. It depends on:

• How much water is in the pot (the quantity).
• The type of material (water in this case).

The formula to calculate heat capacity, denoted as \(C\), is:\[ C = \frac{Q}{\Delta T} \]where:

• \(Q\) is the heat energy supplied.
• \(\Delta T\) is the change in temperature.

Notice that this value increases as the size or mass of the substance increases. Therefore, heat capacity is an extensive property.

Specific Heat

Specific heat refers to the amount of heat per unit mass required to raise the temperature of a substance by one degree Celsius. It's like getting to know how much energy each gram of a material needs to change in temperature, which is quite handy when comparing different materials. The formula for specific heat, indicated by \(c\), is:\[ c = \frac{C}{m} = \frac{Q}{m \times \Delta T} \]where:

• \(m\) is the mass of the substance.
• \(C\) is the heat capacity.

Unlike heat capacity, specific heat doesn't change if you have more or less of the material. Its value is constant for a given substance regardless of the sample size.

Extensive Property

An extensive property is a characteristic that changes with the quantity of the substance you have. It's directly proportional to the size or amount of the sample. For properties classified as extensive:

• The more there is of something, the larger the property value.
• Examples include mass, volume, and, as discussed, heat capacity \((C)\).

This means that if you double the amount of substance, you double the value of its extensive properties.

Intensive Property

In contrast to extensive properties, intensive properties do not depend on the amount of material present. They are intrinsic to the type of material itself. This means:

• These properties remain the same regardless of how much substance you have.
• Examples include density, temperature, and specific heat \((c)\).

Understanding intensive properties helps you determine the material characteristics without needing to know how much is there. Whether you have a drop of water or an ocean, the specific heat remains constant.