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.
See Answer →Obtain an expression for work done in expanding a gas from volume Vi to Vf in an Isobaric process.
See Answer →Derive Mayer's formula: Cp-Cv = R where Cp and Cv are the molar heat capacity at constant pressure and constant volume respectively.
See Answer →Show that for an ideal gas
and
where ẞT is the isothermal compressibility and a is isobaric coefficient of volume expansion. 1
See Answer →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.
See Answer →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.
See Answer →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?
See Answer →Explain the classification of boundaries in a thermodynamic system.
See Answer →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
See Answer →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.
See Answer →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.
See Answer →Using Stokes’ theorem, prove that curl of a conservative force field is zero everywhere.
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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.
See Answer →Determine the work done by a force in taking a particle along the curve x(t) = 2cost;y(t) = 4 sint from t = 0 to
.
If is a constant vector show that
x(
x
)=2
The equation of transverse wave on a rope is
y(x, t) = 10 sin (6.0t − 0.05x)
where y and x are measured in cm and t is expressed in second. Calculate the maximum speed of a particle on the rope.
See Answer →For a damped harmonic oscillation, the equation of motion is
with m = 0.25kg, y= 0.05kgs-1 and 70Nm -1 Calculate (i) the period of motion, (ii) number of oscillations in which its amplitude will become half of its initial value, and (iii) the number of oscillations in which its mechanical energy will drop to half of its initial value.
See Answer →A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is π/2, write expressions for its displacement and velocity. (iii) Calculate the values of maximum velocity and acceleration.
See Answer →The planet Jupiter has an elliptical orbit e =.05 and a semi major axis of 7.8 x 1011 m . Find the energy of the planet and the perihelion and aphelion distances.
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