Question 1

Which equation represents the ideal gas equation for $n$ moles of a gas?

Accepted Answer

The ideal gas equation combining Boyle's law, Charles's law, and Avogadro's law for $n$ moles of a gas is given by $PV = nRT$, where $P$ is pressure, $V$ is volume, $T$ is absolute temperature, and $R$ is the universal gas constant.

Question 2

According to the kinetic theory of gases, the pressure $P$ exerted by an ideal gas of density $\rho$ having RMS speed $v{rms}$ is given by:

Accepted Answer

From kinetic theory, pressure $P = \frac{1}{3} \rho v{rms}^2$.

Question 3

The average translational kinetic energy of a gas molecule is directly proportional to its:

Accepted Answer

The average translational kinetic energy per molecule is $E = \frac{3}{2} kB T$, which shows that it is directly proportional to absolute temperature ($T$).

Question 4

How many degrees of freedom does a monoatomic gas molecule (like Helium) possess?

Accepted Answer

A monoatomic gas molecule can move in three independent spatial directions, so it has 3 translational degrees of freedom and 0 rotational degrees of freedom, making total degrees of freedom = 3.

Question 5

According to the law of equipartition of energy, the energy associated with each degree of freedom per molecule in thermal equilibrium at temperature $T$ is:

Accepted Answer

According to the law of equipartition of energy, for a system in thermal equilibrium, the average energy per degree of freedom per molecule is $\frac{1}{2} kB T$.

Kinetic Theory