(A): The heat capacities of all the diatomic molecules...

(A): The heat capacities of all the diatomic molecules attain a limiting value at higher temperature.
(R): At room temperature, the translational and rotational degrees of freedom become active only at higher temperature.

Key Concepts

Temperature Dependence of Energy Modes

Molecular energy modes are not all active at the same temperature due to the quantization of energy levels. Generally, translational modes are always active, while rotational and vibrational modes require progressively higher temperatures to be significantly excited. This temperature dependence explains why heat capacities reach a limiting value only when all relevant degrees of freedom are activated.

Equipartition Theorem

The equipartition theorem states that, at thermal equilibrium, energy is equally distributed among all active degrees of freedom, with each contributing a fixed amount to the total internal energy. This theorem is fundamental in predicting the heat capacities of gases by relating the number of accessible modes of motion to the energy content of the system.

Degrees of Freedom

Degrees of freedom are the independent ways in which a molecule can store and distribute energy. These include translational, rotational, and vibrational motions. The extent to which each mode contributes to properties like heat capacity depends on the temperature, as some modes require higher thermal energies to be activated.

Heat Capacity

Heat capacity is a measure of the amount of heat required to change the temperature of a system by a given amount. In molecular systems, it reflects how energy is stored in the various modes of motion of the molecules, and its value depends on the number of active energy modes at a specific temperature.

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