MChem Master of Chemistry Master of Chemistry: Physical Chemistry 3

Question 1

The canonical partition function Q for a system of N distinguishable, independent particles is related to the single-particle partition function q by:

Accepted Answer

Q = q^N

Answer

For distinguishable independent particles, the system partition function is simply the product of individual partition functions: Q = q^N.

Question 2

At high temperatures, the heat capacity at constant volume of a diatomic ideal gas approaches (per molecule) according to the equipartition theorem:

Accepted Answer

⁷∕₂ k_B

Answer

A diatomic molecule has 3 translational + 2 rotational + 2 vibrational (kinetic+potential) degrees of freedom, giving C_V = 7/2 k_B at high T.

Question 3

The Boltzmann entropy formula S = k_B ln(Ω) implies that the entropy of a perfect crystal at 0 K is zero because:

Accepted Answer

There is only one accessible microstate (Ω=1)

Answer

A perfect crystal at 0 K has a unique ground state arrangement, so Ω = 1 and S = k_B ln(1) = 0, consistent with the Third Law.

Question 4

The Maxwell-Boltzmann speed distribution for gas molecules predicts that the most probable speed v_p scales with temperature as:

Accepted Answer

v_p ∝ T^(1/2)

Answer

The most probable speed v_p = √(2RT/M) is proportional to the square root of absolute temperature.

Question 5

For an ideal gas undergoing a reversible adiabatic expansion, which relationship between pressure P and volume V holds (γ = C_p/C_v)?

Accepted Answer

PV^γ = constant

Answer

A reversible adiabatic (isentropic) process for an ideal gas obeys PV^γ = constant, derived from the first law with dq = 0.

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Master of Chemistry: Physical Chemistry 3