Browse & Filter

The canonical partition function for an ideal gas is computed and ideal gas equation is derived. A measurement of the Boltzmann constant k is discussed using effusion of gas molecules through a hole. Distribution function of molecules in presence of gravity is as function of height is derived.

$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\average}[2]{\langle#1|#2|#1\rangle}
\newcommand{\Label}[1]{\label{#1}}$

Starting from the time dependent Schr\"{o}dinger equation, an equation of continuity \[{\partial\rho\over\partial t} + \vec{\nabla}.\vec{j}=0\] is derived. Physical interpretation of the continuity equation is given in analogy with charge conservation in electromagnetic theory. The equation of continuity represents conservation of probability in quantum mechanics.

We define the mutual inductance for two loops and self inductance for a loop. We obtain an expression for energy of a circuit with self inductance \(L\)

 Liquid water having a mass of 10 kg and a temperature of
20$^\circ$C is mixed with 2 kg of ice at a temperature of
$-5^\circ$C at 1 atm pressure until equilibrium is reached. Compute
final temperature and the change in entropy of the system 

$ C_p\,\text{(water)}=4.18\times10^3 {\rm K}^{-1}{\rm kg}^{-1}~;~~
C_p{\rm (ice)}=2.09\times10^3{\rm J}\,{\rm kg}^{-1}{\rm K}^{-1}~;~
l_{12}=3.34\times10^5{\rm J}\,{\rm kg}^{-1}$

 Electrodynamics                                              Apr 1, 2019

                                                 Quiz-VI

• Two infinite long wires, carrying currents $I$ and $2I$, pass through points $A,B$ separated by a distance $10L$, as shown in figure below.
  • Sketch a figure to show the directions of the magnetic field due the two wires at a point $P$ at distance $12L$ from the line $AB$.
  • Find the magnitude and direction of the resultant magnetic field due to the two wires at point $P$.
  
• A long straight wire carrying a current $2I$ is placed in the plane having a rectangular loop carrying current $3I$ as shown in the figure.
  • What are the magnitude and directions of magnetic force on the loop the two sides $AD$ and $BC$ due to the current in the straight wire?
  • Divide the side $AB$ into small line elements, write the force on a small line element and hence find the net magnetic force on the side $AB$ due the straight wire.
  • Compute the net force on the loop when $I=10$A, $L=10$ cm, $a=1$cm, $b=80$cm.
  

Electric field due to several charge distributions, listed in the table of contents, is computed using Coulomb’s law.

In a monoatomic crystalline solid each atom can occupy either
a regular lattice site or an interstitial site. The energy of an atom at an
interstitial site exceeds the energy of a atom at a lattice site by an amount
\(\epsilon\). Assume that the number interstitial sites equals the number of
lattice sites, and also equals the number of atoms \(N\). Calculate the entropy
of the crystal in the state where exactly \(n\) of the atoms are at the
interstitial sites. What is the temperature of the crystal in this state,if the
crystal is in thermal equilibrium? If \(\epsilon=1 \text{ev}\) and the
temperature of the crystal is 300K, what is the fraction of the atoms at the
interstitial sites?