BSc Physics SEM V 2018 19 Oct 2018-19 PHYSICS PAPER I MATHEMATICAL IN METHODS IN PHYSICS THERMAL AND STATISTICAL PHYSICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 (a) Attempt any one:
   • (i) | What is a sample space? When do you say a sample space is uniform? 10 Write a uniform sample space for tossing of 2 dice showing all the possible events. Find the probability
   • A) of each sample point. B) that sum of numbers on both the dice is 5
   • C) that sum of numbers on both the dice is divisible by 5
   • D) that numbers on both the dice are same (eg etc )
   • (ii) Explain in brief about Poisson distribution. Derive the equation for 10
   • (b) Attempt any one:
   • (i) | Write probabiliy density function and cumulative distribution function for 5 normal or Gaussian distribution giving the meaning of the terms appearing in the function. Represent it graphically is standard normal (li) random variable x takes the values 0, with the probabilities 5 respectively. Make a table of x; with corresponding probabilities p; Calculate mean x and variance of x
2. Q2 (a) Attempt any one:
   • (i) Explain the method involved in solving a second order non- homogeneous 10 differential equation by successive integration. Hence Write expression for Fourier transform of a function f(x).Hence find 10 Fourier transform of
   • B) Find Fourier Sine transform of f
   • (b) Attempt any one:
   • (i) Write Laplace transform of a function y = f (t) and obtain expressions for 5 the Laplace transform for its derivatives and f” (t) Subject Code: 24116/ Physics: Paper I - Mathematical in Methods in Physics Thermal and Statistical Physics. (R
3. Q3 (a) Attempt any one:
   • (i) | What is mean by reversible and irreversible processes? By taking suitable 10 example, show that the number of accessible microstates increases in an
   • (ii) Show that in a general interaction, between two systems, equilibrium is 10 reached when temperature of the systems becomes equal and pressure of the two becomes equal
   • (b) Attempt any one:
   • (i) | Discuss the concept of phase space. Hence find number of quantum states 5 lying between p and p+dp. Hence p is the momentum
   • (ii) Write notes on partition function. 5
4. Q4 (a) Attempt any one:
   • (i) Derive Maxwell-Boltzmann law of distribution of velocities. 10
   • (b) Attempt any one:
   • (i) Discuss Rayleigh-Jeans formula for black body radiation in short. 5
   • (ii) Explain in short priori probability and thermodynamic probability. 5
5. Q5 (a) Attempt any one:
   • (i) there are 2 black, red balls. ball is drawn at 4 random, what is the probability A) that it is black? B) That it is not red?
   • (ii) consists of 20 students. In how many ways can a president, vice- 4 president, secretary and a treasurer be chosen? In how many ways can a committee of 4 members be chosen from the class of 20 students?
   • (b) Attempt any one:
   • (i) Find the Laplace transform of for t>0 4
   • (c) Attempt any one:
   • (i), . What is ensemble? Show that the ensemble average value of any variable 4 is given by yr
   • (ii) and explain law of thermodynamics. 4
   • (d) Attempt any one:
   • (i) . Calculate the temperature at which the average speed of hydrogen 3 molecule will be the same as that of oxygen molecule at C. Molecular weight of oxygen and hydrogen are 32 and 2 respectively (i1) Derive the formula of root mean square velocity c 3

Read from the scan above, so a character or two may differ. The scan is the original.