Question

True or False? The change in entropy of a substance as its temperature increases depends upon the specific heat of the substance. Explain.

Short answer

True, because entropy change depends on reversible heat exchange, which involves specific heat.

Step-by-step solution

Understanding Entropy and Temperature

Entropy is a measure of disorder or randomness in a system. When the temperature of a substance increases, the kinetic energy of its molecules also increases, leading to a change in entropy.

Role of Specific Heat

The specific heat of a substance is the amount of heat required to change the temperature of a unit mass of the substance by one degree Celsius. It indicates how much energy is needed for a temperature change.

Relationship Between Entropy and Specific Heat

The change in entropy ( ΔS ) is calculated using the formula ΔS = rac{q_{ ext{rev}}}{T} , where q_{ ext{rev}} is the reversible heat exchange. For a finite temperature difference, this heat is often calculated as q = mc ext{ΔT} , where m is the mass, c is the specific heat, and ΔT is the temperature change.

Conclusion

Since the change in entropy depends on the reversible heat exchange, which includes the specific heat, the change in entropy does depend upon the specific heat of the substance.

Key concepts

Specific Heat

Specific heat is a crucial concept in understanding how substances respond to heat energy. It defines the amount of energy required to raise the temperature of 1 kilogram of a substance by 1 degree Celsius. This property varies across different materials and influences how quickly or slowly they can heat up or cool down.
When dealing with specific heat:

• A high specific heat means the substance requires more energy to change its temperature.
• A low specific heat indicates less energy is needed for temperature changes.

For example, water has a high specific heat, which is why it takes longer to heat compared to metals with low specific heat, like copper.

Temperature Change

Temperature change occurs when a substance absorbs or releases heat. This can lead to either an increase or a decrease in temperature, often measured in degrees Celsius or Kelvin.
Here's how it works:

• When a substance gains heat, its temperature rises.
• Losing heat results in a temperature decrease.

The amount of temperature change depends on the substance's specific heat and the mass of the substance involved in the process. If two substances receive the same amount of heat, the one with the lower specific heat will experience a more significant temperature change.

Reversible Heat Exchange

Reversible heat exchange is a thermodynamic concept where heat is transferred between a system and its surroundings in such a way that the process can be reversed without leaving any net change in either system or surroundings. It is an ideal process used in theoretical models.
In reversible heat exchange:

• All changes occur infinitesimally slowly, maintaining equilibrium throughout.
• The entropy change (\( \Delta S \)) of a system is given by the relationship: \( \Delta S = \frac{q_{\text{rev}}}{T} \)

Here, the heat added reversibly (\( q_{\text{rev}} \)) is divided by the temperature (\( T \)) of the system.

Kinetic Energy

Kinetic energy is the energy of motion. In the context of thermodynamics, it refers to the energy possessed by the particles of a substance due to their motion. As temperature increases, the kinetic energy of these particles typically increases as well.
Key points about kinetic energy:

• It is directly proportional to the temperature of a substance.
• Higher kinetic energy means that particles move faster.

For example, when a substance is heated, its particles vibrate more vigorously, leading to increased kinetic energy and, consequently, a higher temperature.

Disorder or Randomness

In thermodynamics, disorder or randomness is referred to as entropy. It quantifies the number of possible arrangements of particles in a system. A system with more disorder has higher entropy.
Consider these aspects:

• An increase in temperature generally leads to increased entropy as particles move more freely and occupy more space.
• Entropy gives insight into the degree of randomness and can predict the direction of spontaneous processes.

Overall, the concept of entropy helps us understand how energy disperses in a system and why some processes occur naturally.