Define mean free path. Obtain its expression under zeroth order approximation.
Mean free path, average distance an object will move between collisions. The actual distance a particle, such as a molecule in a gas, will move before a collision, called free path, cannot generally be given because its calculation would require knowledge of the path of every particle in the region.
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Four particles are to be distributed in 5 states. Calculate the number of ways in which this distribution can be done if the particles obey:
(i) M-B statistics and (ii) B-E statistics.
Define viscosity. Discuss the effect of temperature and pressure on viscosity.
What is Joule-Thomson effect? Write an expression for Joule-Thomson coefficient for a van der Waals’ gas and discuss the significance of a and b in this expression.
Two systems have thermodynamic probabilities of 3.0 1027 and 1.8
1028 respectively. Calculate the entropies of the individual systems and as well as their composite system and verify the Boltzmann relation.
Derive the single-particle partition function for an ideal monatomic gas consisting of N identical particles occupying a volume V. Obtain expressions for the entropy and pressure of this system.
What do you understand by intensive and extensive variables of a system? State with reasons, which of the following variables are intensive and which are extensive?
i) Number of gas molecules enclosed in a box;
ii) Density of gas in a box;
iii) Wavelength of radiation emitted by a black body at temperature T;
iv) Intensity of radiation emitted by a black body at temperature T.
Derive an expression for efficiency of a Carnot engine using T-S diagram. A Carnot engine has an efficiency of 50 percent when its sink temperature is at 27 ºC. Calculate the change in source temperature for increasing its efficiency to 60 percent.