Question

Is the specific heat capacity of a substance an intensive or extensive property? Explain.

Short answer

Specific heat capacity is an intensive property because it does not depend on the amount of substance.

Step-by-step solution

Understanding Intensive and Extensive Properties

Intensive properties are those that do not depend on the amount of substance present. Examples include temperature, density, and boiling point. Extensive properties, on the other hand, do depend on the amount of substance. Examples include mass, volume, and total energy.

Defining Specific Heat Capacity

Specific heat capacity is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). The formula for specific heat capacity is given by \[ c = \frac{q}{m \Delta T} \] where \( q \) is the heat added, \( m \) is the mass, and \( \Delta T \) is the change in temperature.

Determining Dependency on Amount of Substance

Evaluate whether specific heat capacity depends on the amount of substance present. Since the specific heat capacity is defined per unit mass, it does not matter how much of the substance you have; the specific heat capacity remains the same.

Conclusion

Since the specific heat capacity remains the same regardless of the amount of substance, it is an intensive property.

Key concepts

intensive properties

Properties of matter can be broadly categorized into two types: intensive and extensive properties. Intensive properties are those that do not depend on the amount of the substance present. This means that no matter how much or how little of the substance you have, an intensive property remains unchanged. Examples of intensive properties include:

• Temperature
• Density
• Boiling Point

For instance, if you have a cup of water or a whole pot of water, its temperature remains the same, provided it is at the same state. It is essential to identify intensive properties accurately as they help in understanding and characterizing substances better. Specific heat capacity is a key intensive property which we'll explore further.

extensive properties

In contrast to intensive properties, extensive properties depend on the amount of the substance present. These properties change when the quantity of the material changes. Examples of extensive properties include:

• Mass
• Volume
• Total Energy

For example, if you have more water, you will have a greater mass and volume of water. Extensive properties are additive for functionally homogeneous systems. This means that if you have two separate amounts of a substance, their extensive properties, such as the total mass, will add up if you combine them. Understanding the difference between intensive and extensive properties helps in various scientific calculations and practical applications, especially when determining the behavior of materials under different conditions.

heat capacity formula

One of the significant intensive properties we often encounter in physics and chemistry is specific heat capacity. Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). The specific heat capacity formula is:


$c=\frac{q}{m⁚\Delta T}$

Here:

• $q$ is the heat added
  
• $m$ is the mass
  
• $\mathrm{\Delta T}$ is the change in temperature
  

This formula shows that specific heat capacity is calculated on a per unit mass basis, making it an intensive property. This means that regardless of the amount of a substance, its specific heat capacity remains the same. This characteristic makes it very useful in thermal calculations, especially when dealing with phase changes or energy transfer processes.