The energy of a capacitor is 4.0 _uJ after it has been charged by a 1.5 V battery. Calculate its energy when it is charged by a 6.0 V battery.

Derive Planck’s law of radiation and hence obtain Rayleigh-Jeans law and Wien’s law.

When two phases of a substance coexist in equilibrium at constant temperature and pressure, their specific Gibb’s free energies are equal. Using this fact, obtain Clausius-Clapeyron equation. 

Explain the phenomenon of polarisation of a dielectric. Show that, when a dielectric material is filled between the plates of a capacitor, the value of capacitance increases by factor of K, the dielectric constant of the material.

Define thermodynamic potentials. Derive Maxwell’s relations from thermodynamic potentials. 

Two particles carrying 4C and - 2C charges are placed on a 1 m long straight wire. Determine the point on the line joining these particles where the electric potential is zero with reference to the positively charged particle.

With the help of entropy – temperature diagram of Carnot cycle, obtain an expression of efficiency of a Carnot engine. A Carnot engine has an efficiency of 50%. It operates between reservoirs of constant temperature with temperature difference of 80 K. Calculate the temperature of the low-temperature reservoir in Celsius.

Obtain an expression for work done in expanding a gas from volume V_i to V_f in an Isobaric process. 

Derive Mayer's formula: C_p-C_v = R where C_p and C_v are the molar heat capacity at constant pressure and constant volume respectively.

Show that for an ideal gas

 and 

where ẞ_T is the isothermal compressibility and a is isobaric coefficient of volume expansion. 1

Determine the electrostatic force and electrostatic field on a charged particle located at A in the Figure given below due to the charged particles situated at B and C. The value of the charge on each of these particles is indicated in the Figure.

Express your result both in the unit vector notation and as magnitude.

State Zeroth law of thermodynamics. How does this law introduces the concept of temperature. Write parametric as well as exact equation of state for one mole of a Ideal gas and stretched wire. 

Explain with the help of diagrams what spherically and cylindrically symmetric charge distributions are. What is the electric field at a point inside a hollow metallic sphere of radius R having volume charge density p?

Explain the classification of boundaries in a thermodynamic system.

What is Brownian motion? Discuss Perrin's method for determination of Avogadro number in Brownian motion. How can this method be used to estimate the mass of molecule

Determine the directional derivative of the scalar field  in the direction   at the point (1,-1, 2).

The average speed of hydrogen molecules is 1850 ms-1. The radius of a hydrogen molecule is 1.40x10^-10m. Calculate (i) Collision cross-section, (ii) collision frequency, and (iii) mean free path. Take n = 3x10²⁵m^-3.

Write the assumptions made by Maxwell to derive the expression for distribution function of velocities. Hence derive the expression of Maxwellian distribution function for molecular speeds. Plot Maxwellian distribution function as a function of molecular speed.

Using Stokes’ theorem, prove that curl of a conservative force field is zero everywhere.

Discuss Regnault's experiments on Hydrogen, nitrogen and carbon dioxide for 273 K. Also discuss the Andrews experiments for CO₂ on the p-V diagram at various temperatures.