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.
    Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

      • The total charge of the two spheres is conserved.
      • Both spheres attain the same potential.
      • The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2)}{(r_1 + r_2)}$
      • The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2) (r_1 + r_2)}{r_1 r_2}$

    • 2.
      Write two advantages of reflecting telescope over refracting telescope.


        • 3.
          A charged particle $+q$ in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to both velocity $\vec{v}$ of the charged particle and the magnetic field $\vec{B}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses $m$ and $\frac{m}{2}$ having charges $-q$ and $+2q$ respectively. They are accelerated from rest through the same potential difference $V$ and acquire kinetic energy $K_1$ and $K_2$. Then they enter in a region of uniform magnetic field $\vec{B}$ perpendicular to their velocities.


            • 4.
              Read the following paragraph and answer the questions that follow.
              A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.


                • 5.
                  The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.


                    • 6.
                      Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance $U = \frac{1}{2}CV^2$, where symbols have their usual meanings.
                      Two capacitors, one of $3 \ \mu$F and the other of $6 \ \mu$F, are connected in series in the circuit as shown in the figure, for a long time. }

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