Statistical Mechanics - Specific Heat Capacity

In summary, the specific heat capacity goes to zero as temperature goes to zero because at absolute zero, the average kinetic energy of particles is zero, meaning that even a small amount of added heat will result in a relatively large increase in kinetic energy, leading to a near-zero specific heat capacity. This can be explained using the fundamental thermodynamic identity and the third law of thermodynamics.
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Homework Statement



Give an physical explanation to why the specific heat capacity goes to zero as temperature goes to zero.

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The Attempt at a Solution



I was simply thinking that around absolute zero the average kinetic energy of the particles should be zero, meaning that the atoms in the solid would be pretty much at a halt. Thus, even if we just add an infinitesimal amount of heat the increase in average kinetic energy would be relatively big, implying that the specific heat capacity goes to zero. Even I myself think that that last part is flawed, so I'm looking for any better explanation of this fenomenon. Any help appreciated!
 
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using the fundumental thermodynamic identity, and the third law of thermodynamics, one requires that the heat capacity (at constant pressure) becomes and infinitisimal quantity at absolute zero.
 

Related to Statistical Mechanics - Specific Heat Capacity

1. What is statistical mechanics and how does it relate to specific heat capacity?

Statistical mechanics is a branch of physics that uses statistical methods to explain the behavior of a large number of particles or systems. Specifically, it studies the relationship between the microscopic properties of particles and the macroscopic properties of a system, such as temperature and energy. The concept of specific heat capacity, which is the amount of heat needed to raise the temperature of a substance by one degree, can be explained using statistical mechanics by considering the energy distribution and interactions of particles within a system.

2. How is specific heat capacity affected by the number of particles in a system?

The specific heat capacity of a system is directly proportional to the number of particles in that system. This is because more particles means more interactions and a larger energy distribution, resulting in a higher specific heat capacity. This relationship is described by the equipartition theorem, which states that the average energy of a particle in a system is directly proportional to the temperature and the number of degrees of freedom (or independent ways the particle can store energy).

3. What is the difference between specific heat capacity at constant volume and at constant pressure?

Specific heat capacity at constant volume (CV) is the amount of heat required to increase the temperature of a substance at constant volume, while specific heat capacity at constant pressure (CP) is the amount of heat required to increase the temperature of a substance at constant pressure. The main difference between the two is that specific heat capacity at constant pressure takes into account the work done by the substance as it expands, while specific heat capacity at constant volume does not. This means that CP is generally higher than CV for a given substance.

4. How does the specific heat capacity of a gas differ from that of a solid or liquid?

The specific heat capacity of a gas is generally higher than that of a solid or liquid, as gases have more degrees of freedom and therefore more ways to store energy. This means that gases require more energy to increase their temperature by one degree compared to solids and liquids. Additionally, the specific heat capacity of a gas is also dependent on its molar mass, with heavier gases having a lower specific heat capacity due to their slower molecular motion.

5. Can specific heat capacity be affected by external factors?

Yes, specific heat capacity can be influenced by external factors such as pressure, temperature, and the presence of impurities. For example, increasing the pressure on a substance can decrease its specific heat capacity, as the molecules are forced closer together and have less freedom to move and store energy. Similarly, adding impurities to a substance can disrupt the energy distribution and affect its specific heat capacity. The specific heat capacity of a substance also changes with temperature, as the energy distribution and molecular motion of particles are altered.

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