Solve your IGNOU Doubts

Question:

Consider that two ideal gases having n₁ moles are n₂ moles are enclosed in two separate containers at constant temperate T and pressure P. It these two gases mix, obtain an expression for the entropy of mixing per mole of mixture.

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Question:

Obtain an expression of coefficient of volume expansion for one mole of van der Waals’ gas.

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Question:

Obtain the expressions of work done for an ideal gas (i) in an isothermal expansion (ii)) in an adiabatic process.

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Question:

State the zeroth law of thermodynamics. Explain how the zeroth law introduces the concept of temperature.

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Question:

i) What are intensive and extensive variables for thermodynamic systems? Write two examples of each.
ii) Represent an (a) isobaric (b) isochoric (c) isothermal and (d) a cyclic process on p-V indicator diagram.

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Question:

A mass of an ideal gas $(\gamma = 1.5)$ at $27^\circ\text{C}$ is suddenly compressed to four times its original pressure. Calculate the final temperature of the gas.

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Question:

Write the expressions of an ideal gas and van der Waals’ equation. 10 moles of nitrogen gas occupy a volume of $5 \times 10^{-3}\text{ m}^3$ in a vessel at $27^\circ\text{C}$ . Calculate the pressure exerted by the molecules, if it is assumed to obey van der Waals’ equation. Compare this Value with that obtained using ideal gas law.
Given: $a = 1.39 \times 10^{-6}\text{ atm m}^6\text{ mol}^{-2}$ ,
$b = 39.1 \times 10^{-6}\text{ m}^3\text{ mol}^{-1}$
and $R = 8.2 \times 10^{-5}\text{ atm m}^3\text{ K}^{-1}\text{ mol}^{-1}$ .

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Question:

What is Brownian motion? Write its two examples. Show that during sedimentation, particles concentration decreases exponentially as height increases.

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Question:

Define mean free path? Obtain an expression of mean free path for zeroth order approximation.

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Question:

What is most probable speed? Using the expression of the number of molecules in a Maxwellian gas in the range v to v + dv as
$$dN_v = 4\pi N \left( \frac{m}{2\pi k_BT} \right)^{3/2} v^2 \exp \left[ - \left( \frac{mv^2}{2k_BT} \right) \right] dv$ $
Obtain an expression for most probable speed.

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Question:

Calculate v_rms for helium atoms at 300K. At what temperature will oxygen molecules have the same value of v_rms? Take $m_{He} = 6.67 \times 10^{-27}\text{ kg}$ .

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Question:

The refractive indices of the core and cladding materials of an optical fibre are 1.51 and 1.39, respectively. Calculate the numerical aperture and light gathering capacity of the fibre.

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Question:

Two energy levels of an atomic system are separated by energy corresponding to frequency $3.0 \times 10^{14}\text{ Hz}$ . Assume that all atoms are in one or the other of these two energy levels, compute the fraction of atoms in the upper energy level at temperature $400\text{ K}$ . Take $k_B = 1.38 \times 10^{-23}\text{ JK}^{-1}$ and $h = 6.6 \times 10^{-34}\text{ Js}$ .

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Question:

An atomic system consisting of two energy levels, with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.

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Question:

Discuss Rayleigh’s criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.

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Question:

A plane light wave of wavelength $580\text{ nm}$ falls on a long narrow slit of width $0.5\text{ mm}$ . (i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to $0.2\text{ mm}$ ? (iii) If a convex lens of focal length $0.15\text{ m}$ is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.

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Question:

A plano-convex lens of radius $1.0\text{ m}$ is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the $10^{\text{th}}$ and $5^{\text{th}}$ dark rings in the reflected light are $4.50 \times 10^{-3}\text{ m}$ and $3.36 \times 10^{-3}\text{ m}$ . Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the $5^{\text{th}}$ ring changes to $3.0 \times 10^{-3}\text{ m}$ . Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is $589\text{ nm}$ .

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Question:

Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment.

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Question:

Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.

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Question:

Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.

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