Bose-Einstein condensation.

Establish van der Waals’ equation of state for a real gas. Plot van der Waals’ equation of state on p-V diagram.

Define mean free path of a molecule in a gas. Derive the law of distribution of free paths. 

Calculate the temperature at which the root mean square speed of hydrogen and oxygen molecules will be equal to their escape velocities from the earth's gravitational field. The radius of the earth is 6400 km.

Take N_A=6x10²⁶ mol^-1, g-9.8ms^-2, kg-1.38x10²³JK^-1

List the differences between first and second order phase transitions. What are the characteristics of lambda transition? 

Using Maxwell's relations, derive the first and second energy equations. 

The modulus of rigidity of a wire is

The following measurements are made for L, r and  / N

r = 1.5  0.05 mm

L = 400  2 mm

 = 6.00  0.20 rad N^-1 m^-1

Obtain the best value of .

The efficiency of a Carnot engine is 30%. Its efficiency is to be raised to 60% By how much must the temperature of the source be increased if the sink is at 27°C? 

A website has on the average two hits per hour. Assuming a Poisson distribution for the number of hits per hour (X), calculate the probability that there are at most three hits.

Draw a Carmot cycle on p- diagram. Show that the amount of heat absorbed (rejected) in a reversible cycle is proportional to the temperature of source (sink).

Using the first law of thermodynamics for an adiabatic process, establish the relation PV=K, where y is the ratio of heat capacity at constant pressure to that at constant volume. Plot this equation on a p- diagram. What will be its slope?

Derive an expression for the work done by a gaseous system for an isothermal expansion of an ideal gas. 

Explain the working of a platinum resistance thermometer with the help of a neat and labelled diagram.

An athlete is running in four races and in each race she has a 60% chance of winning. What is the probability that she will win at least two races?

Using the partition function for an ideal gas made up of N indistinguishable particles, obtain Sackur-Tetrode equation.

Calculate the most probable speed, average speed and the root mean square speed for gas molecules at 300 K. The mass of gas molecule is 5 x 10 ^-26 kg and k_B = 1.38 x 10 ^-23JK ^-1.

random variable X has the following probability distribution:

Determine the value of the constant k and E(X).

One mole of an ideal gas expands isothermally to five times its initial volume. Calculate the entropy change in terms of R, the gas constant. 

A sonometer wire having cross-sectional area 0.85 x 10^-6m² is stretched between two rigid supports 1.2 m apart. A tension of 20 N is applied at its free end. If the temperature is reduced by 12°C, calculate the final tension in the wire. Take coefficient 1.5 x tof linear expansion (a) and isothermal Young's modulus (y) to be 1.5x10^-5 K ^-1 and 2.0 x 10¹¹ Nm ^-2,respectively.

The construction of a building may be delayed by a strike. Suppose that the probability that there will be a strike is 0.70, the probability that the construction

will be completed on time if there is no strike is 0.90 and the probability that the building will be completed on time if there is a strike is 0.40, what is the probability that the construction will be completed on time.