Question

Distinguish among specific heat capacity, molar heat capacity, and heat capacity.

Short answer

Specific heat capacity: heat per gram; Molar heat capacity: heat per mole; Heat capacity: total heat for object.

Step-by-step solution

- Define Specific Heat Capacity

Specific heat capacity, often simply called specific heat, is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or one kelvin. It is usually denoted by the symbol \( c \) and its unit is \( J/g \cdot \degree C \) or \( J/g \cdot K \).

- Define Molar Heat Capacity

Molar heat capacity is the amount of heat needed to raise the temperature of one mole of a substance by one degree Celsius or one kelvin. It is denoted by the symbol \( C_m \) and its unit is \( J/mol \cdot \degree C \) or \( J/mol \cdot K \).

- Define Heat Capacity

Heat capacity is the total amount of heat required to raise the temperature of an entire object or substance by one degree Celsius or one kelvin. It is denoted by \( C \) and is usually expressed in units of \( J/ \degree C \) or \( J/K \). Heat capacity depends on the mass and the type of material of the object.

- Comparison and Summary

To summarize, specific heat capacity is heat per unit mass, molar heat capacity is heat per unit mole, and heat capacity is the total heat for the whole object regardless of mass. Specific heat capacity and molar heat capacity are intrinsic properties, while heat capacity is an extensive property that depends on the amount of the substance.

Key concepts

Specific Heat Capacity

Specific heat capacity describes how much heat is needed to change the temperature of a unit mass of a substance by one degree. This property is intrinsic, meaning it does not depend on the amount of substance, but rather its nature. For example, water has a higher specific heat capacity compared to metals like iron. This is why water changes temperature more slowly than iron. The formula for specific heat capacity is usually represented as follows:
\( q = m \times c \times \triangle T \)
where:

• \( q \) is the heat added
• \( m \) is the mass of the substance
• \( c \) is the specific heat capacity
• \( \triangle T \) is the change in temperature

This equation shows that specific heat capacity is essential for understanding how different substances absorb and retain heat.

Molar Heat Capacity

Molar heat capacity is another intrinsic property, similar to specific heat capacity, but it focuses on the amount of heat needed to raise the temperature of one mole of a substance by one degree. One mole is a specific number of molecules or atoms, precisely Avogadro's number which is approximately \( 6.022 \times 10^{23} \) particles. Because molar heat capacity deals with moles instead of mass, it helps chemists and physicists better understand heat behavior at a molecular level.
Here is the formula for molar heat capacity:
\( q = n \times C_m \times \triangle T \)
where:

• \( q \) is the heat added
• \( n \) is the number of moles
• \( C_m \) is the molar heat capacity
• \( \triangle T \) is the change in temperature

Molar heat capacity helps in analyzing reactions and phase changes on a particle level, offering a more precise understanding than specific heat capacity for specific applications.

Heat Capacity

Heat capacity is the total quantity of heat required to raise the temperature of an entire body by one degree. Unlike specific heat capacity and molar heat capacity, heat capacity is an extensive property. This means it depends not just on the nature of the material, but also on its mass or amount. Heat capacity is particularly useful when considering large systems, such as the heat needed to warm up an entire swimming pool or building.
The formula for heat capacity is straightforward:
\( C = \frac{q}{\triangle T} \)
where:

• \( C \) is the heat capacity
• \( q \) is the heat added or removed
• \( \triangle T \) is the change in temperature

Since it takes into account the mass of the object, larger objects will naturally have higher heat capacities. Heat capacity is critical for engineering and design, particularly when creating systems for heating and cooling.