Statistical Physics: Need, Application & Microscopic Laws

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Statistical Physics is the study of the macroscopic parameters of a system in equilibrium based on the knowledge gained from its microscopic properties using the laws of mechanics. It is a branch of physics that has developed from statistical mechanics. The aim of statistical physics is to use the understanding of microscopic laws governing the motion of atoms and another law of statistical physics to give the expression of free energy. 

Keyterms: Macroscopic parameters, Atoms, Energy, Mechanics, Motion, Thermal equilibrium states, Non-equilibrium states, Thermodynamics

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What is Statistical Physics?

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Statistical Physics is a branch of physics that has developed from statistical mechanics. The aim of statistical physics is to use the understanding of microscopic laws governing the motion of atoms and another law of statistical physics to give the expression of free energy. Statistical physics involves the study of both thermal equilibrium states and non-equilibrium states. This is unlike thermodynamics, which studies macroscopic systems in equilibrium from a macroscopic perspective without taking into consideration the microscopic parameters.

Statistical Physics deals with microscopic laws

Statistical Physics deals with microscopic laws

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Need for a Statistical Description in Physics

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Statistical Physics provides a link between the macroscopic and microscopic views. For example, in the study of gases, examining the statistical distribution of particle velocities gives an understanding of the relation between the macroscopically observable quantities such as volume, temperature and pressure. Listed below are some examples where the statistical description has been beneficial.

  • Applying the statistical approach to thermodynamics can help gain a better understanding of entropy. For example, the temperature can be statistically understood as the average kinetic energy of atoms in a matter.
  • In quantum physics, the application of statistics to describe processes such as Brownian motion has been useful for the derivation of the “path-integral” formulation.

Brownian Motion

Brownian Motion

  • Maxwell-Boltzmann statistics are used to understand the distribution of particles at various energy levels as a function of temperature. This helps to get an insight into the processes, such as diffusion.

The study of statistics in all scientific disciplines provides a practical set of tools to test hypotheses and to estimate confidence intervals on aggregate data. It forms the basis of the design of experiments, interpretation of data and correlation of information, which lies at the core of the development of modern science.

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Application of Statistical Physics

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  • Maxwell’s distribution of molecular velocity is based on statistical physics.
  • With the help of statistical physics, Gibbs explained thermodynamics.

Things To Remember

  • Statistical physics is a branch of physics that grew from statistical mechanics.
  • It gives us the expression of free energy by using microscopic laws of a system along with another law of statistical physics.
  • By using the knowledge of the microscopic properties, statistical physics gives a better understanding of the macroscopic parameters of a system in equilibrium.
  • It forms a link between the macroscopic and microscopic parameters of a system.
  • Statistical physics forms the basis for designing scientific experiments, data interpretation and correlating information.

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Sample Questions

Ques: Explain statistical physics. (2 marks)

Ans: Statistical physics is a branch of science derived from statistical mechanics. It uses the laws of mechanics with the understanding of the microscopic properties to study the macroscopic parameters of a system in equilibrium. So, it uses the fact that matter comprises atoms. By using the microscopic laws along with another law of statistical physics, it gives an expression of free energy. Statistical physics involves the study of both thermal equilibrium states and non-equilibrium states.

Ques: State some applications of statistical physics. (2 marks)

Ans: Some applications of statistical physics are:

  • Gibbs gave an explanation for thermodynamics with the help of statistical physics.
  • For Maxwell’s distribution of molecular velocity, the application of statistical physics was to understand the distribution of molecules in an assembly.

Ques: Which law gives the distribution of particles at different energy levels as a function of temperature? (2 marks)
(A) Faraday’s law
(B) Gibbs’ law
(C) Plank’s law
(D) Maxwell-Boltzmann statistics

Ans: D. Maxwell-Boltzmann statistics

Maxwell-Boltzmann statistics are used to explain the distribution of particles at different energy levels as a function of temperature. It also helps to get an insight into the processes such as diffusion.

Ques: State whether this statement is true or false. Why? (2 marks)
Statement: Statistical physics provides a link between macroscopic and microscopic views of a system.

Ans: The given statement is true. Statistical physics aims to understand the macroscopic parameters of a system in equilibrium by using the knowledge of their microscopic properties. It uses the fact that matter consists of atoms. And thus, forming a link between macroscopic and microscopic parameters.

Ques: How can statistical physics be used to study gases? (2 marks)

Ans: In the study of gases, statistical physics can be useful to examine the statistical distribution of particle velocities. And also to understand their relationship with macroscopic quantities such as pressure, temperature and volume.

Ques: Which of the following branches of physics evolved from statistical mechanics? (2 marks)
(A) Quantum Mechanics
(B) Statistical Physics
(C) Mechanical Physics
(D) Modern Physics

Ans: B. Statistical Physics

Statistical physics is a branch of physics that originated from statistical mechanics, which uses statistics, probability theory and mathematical tools to deal with large approximations to solve physical problems. 

Ques: Statistical physics uses the laws of mechanics to study the (2 marks)
(A) macroscopic parameters
(B) microscopic parameters
(C) constant parameters
(D) None of the above

Ans: A. macroscopic parameters

Statistical physics uses the laws of mechanics to study macroscopic parameters. It uses the knowledge of microscopic properties to get a better understanding of these macroscopic parameters. To do so, it utilizes the fact that matter is composed of atoms.

Ques: As per statistical physics, matter consists of (2 marks)
(A) air
(B) atoms
(C) water
(D) none of the above

Ans: B. atoms

Statistical physics uses the fact that matter consists of atoms. Through the law of mechanics, it uses the microscopic properties of a system to understand its macroscopic parameters. It creates a link between the macroscopic and microscopic properties of the system.

Ques. What are Free electrons? (2 marks)

Ans. Free Electrons In metals, the electrons in the outer shells (valence electrons) are loosely bound to the atoms, hence they are free to move easily within the metal surface but cannot leave the metal surface. Such electrons are called free electrons.

Ques. What are the laws of Photoelectric Emission? (3 marks)

Ans. 

  • For a given material and a given frequency of incident radiation, the photoelectric current number of photoelectrons ejected per second is directly proportional to the intensity of the incident light.
  • For a given material and frequency of incident radiation, saturation current is found to be proportional to the intensity of incident radiation, whereas the stopping potential is independent of its intensity.
  • For a given material, there exists a certain minimum frequency of the incident radiation below which no emissions of photoelectrons take place. This frequency is called threshold frequency.

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CBSE CLASS XII Related Questions

  • 1.
    The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

      • \( \frac{q}{4 \pi \epsilon_0 l^2} \) pointing along MA
      • \( \frac{q}{\pi \epsilon_0 l^2} \) pointing along AM
      • \( \frac{q}{2 \pi \epsilon_0 l^2} \) pointing along AM
      • Zero

    • 2.
      A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.


        • 3.
          Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.


            • 4.
              If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.


                • 5.
                  Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))


                    • 6.
                      If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

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