Final answer:
In thermodynamics, energy is directly proportional to the degrees of freedom. Each degree contributes an amount of energy based on temperature and Boltzmann's constant, affecting the internal energy and heat capacity of a gas.
Step-by-step explanation:
The question relates to the concept of degrees of freedom in the context of thermodynamics and statistical mechanics. Degrees of freedom are fundamental in determining the amount of energy in a system. In thermodynamics, each degree of freedom contributes a fixed amount of energy (kBT/2 per degree of freedom) to the system's internal energy, where kB is Boltzmann's constant and T is the temperature in Kelvin.
Therefore, the correct answer to the given multiple-choice question is that energy is directly proportional to degrees of freedom. In the case of an ideal monatomic gas, the molecules have three translational degrees of freedom, contributing to the calculation of the molar heat capacity at constant volume, Cy = d/2 R, where d is the number of degrees of freedom (d=3 for monatomic gases).
This principle also helps explain kinetic energy in macroscopic objects, like cars, where kinetic energy is directly proportional to the square of the velocity, explaining why accelerating a car from 20 mph to 40 mph quadruples its kinetic energy.