Canonical Ensemble Parameters Explained
The canonical ensemble in statistical mechanics describes a system that is in thermal equilibrium with a heat bath. This means the system has a fixed number of particles, a fixed volume, and exchanges energy with the surroundings, maintaining a constant temperature.
Identifying Constant Variables
For a system described by the canonical ensemble, the parameters that remain constant are:
- Particle Number ($N$): The total count of particles within the system is fixed.
- Volume ($V$): The space occupied by the system is constant.
- Temperature ($T$): The system is in thermal contact with a reservoir at a constant temperature $T$.
Ensemble Comparison
Other common ensembles have different constraints:
- Microcanonical Ensemble: Constant $N, V, E$ (Energy).
- Grand Canonical Ensemble: Constant $\mu$ (Chemical Potential), $V, T$.
- Isothermal-Isobaric Ensemble: Constant $N, P$ (Pressure), $T$.
Conclusion
Based on the definition, the parameters kept constant for a canonical ensemble are particle number ($N$), volume ($V$), and temperature ($T$). This corresponds to Option 1.
Important Questions from Statistical Thermodynamics
- The molar partition Function of the system is :
- An approximate partition function $Q(N,V,T)$ of a gas is given below.
$Q(N,V,T) = \frac{1}{N!} (\frac{2\pi mk_B T}{h^2})^{3N/2} (V-Nb)^N$
The equation of state(s) for this gas is/are
[Note: $b$ is a parameter independent of volume.] - The correct statement(s) related to an ensemble is (are):
- The moment of inertia of a homonuclear diatomic molecule is $7.5 \times 10^{-45} \text{ kg m}^2$. Its rotational partition function at 500 K is ________.
- For ortho-hydrogen, the nuclear wavefunction and the rotational quantum number, respectively, are
