Heat capacity Exam

A molecule has $f$ degrees of freedom. If it behaves classically, what is the average energy stored per degree of freedom?

Quantum mechanical effects cause specific heat capacities to fall at lower temperatures. What is the primary reason for this phenomenon?

For an ideal gas, Mayer's relation states that the difference between the molar heat capacity at constant pressure ($C_{p,m}$) and the molar heat capacity at constant volume ($C_{v,m}$) is equal to the universal gas constant, R. If a gas has $C_{v,m} = \frac{3}{2}R$, what is its molar heat capacity at constant pressure, $C_{p,m}$?

Calculate the molar heat capacity at constant pressure, $C_{P,m}$, for an ideal monatomic gas if its molar heat capacity at constant volume, $C_{V,m}$, is $12.5 \, J/(mol \cdot K)$. Use $R = 8.314 \, J/(mol \cdot K)$.

Consider a hypothetical molecule with 3 translational, 2 rotational, and 2 vibrational degrees of freedom. If this molecule behaves as an ideal gas, what would be its molar heat capacity at constant volume, $C_{V,m}$, in terms of $R$?

A solid material has a molar heat capacity of $2.5R$ per mole of atoms at room temperature. If this material is composed of light, tightly-bound atoms, what quantum mechanical effect is most likely responsible for its heat capacity being lower than the Dulong-Petit limit of $3R$?

For an ideal gas, the relationship $C_p - C_v = nR$ is valid. If a gas has a molar heat capacity at constant volume ($C_{v,m}$) of $20.8 \, J/(mol \cdot K)$ and a molar heat capacity at constant pressure ($C_{p,m}$) of $29.1 \, J/(mol \cdot K)$, what is the approximate value of the universal gas constant, R, in $J/(mol \cdot K)$?

The internal energy of a closed system is described by the equation $dU = dQ + dW$. If the system undergoes a process at constant volume, what term in this equation vanishes, leading to the definition of heat capacity at constant volume, $C_V$?

According to the International System of Units (SI), what is the unit for heat capacity?

Consider two identical samples of a substance, one at $10 \, K$ and the other at $100 \, K$. Which of the following statements is most likely true regarding their specific heat capacities, assuming no phase transitions occur?