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[QUE/SM-06001] SM-PROBLEMNode id: 5072pageConsider a photon gas in two dimensions at temperature T in area A. Find the energy density $u(\omega)$ as a function of temperature and various physical constants. Show that the total energy is proportional to $T^3$. ( you can assume that the internal degree of freedom is 1
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[QUE/TH-01004] TH-PROBLEMNode id: 5189page
Express the temperatures given below in $^\circ C,R$, and $^\circ F$. Write your answers in form of table.
- (a) Triple point of Hydrogen 13.81 K
- (b) Boiling point of Ne 27.102 K
- (c) Boiling point of Oxygen 90.188 K
- (d) Melting point of zinc 692.664
- (e) Melting point of gold 1337.58
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22-10-17 15:10:45 |
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[2008EM/HMW-02]Node id: 5399page |
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[2003SM/LNP-18] Lecture-18--Grand Canonical Ensemble — Summary and ApplicationsNode id: 5543pageThe main result for grand canonical ensemble are summarized. The Planck’s law and the Stephan Boltzmann law for black body radiation are derived.
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22-07-07 07:07:35 |
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[1998TH/LNP-39]-Statistical Mechanics of an Ideal GasNode id: 5607page |
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[NOTES/ME-06002]-Using graph of $V(x)$ to find motionNode id: 5675page |
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[NOTES/EM-10001]-Overview of Electrodynamics EquationsNode id: 5731pageImportant equations of electrodynamics,the equation of continuity, the Lorentz force and the Maxwell's equations are summarized.
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22-08-26 19:08:47 |
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[NOTES/QCQI-01001] Binary Number RepresentationNode id: 5016page |
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[QUE/TH-05003] TH-PROBLEMNode id: 5158pageConsider $n$ mole of ideal gas whose entropy is given by $$ \frac{n}{2}\left[c_1\,+\,5R{\ln}\frac{U}{n}\,+\,2R{\ln}\frac{V}{n} \right]$$ where $R$ is the univeral gas constant, $U$ the internal energy, $V$ the volume and $c_1$ a constant.
- Calculate the specific heats $c_V$ and $c_p$
- A room is at a temperature $273^o$ K which is in equilbrium with the surroundings. One hour after turning on a heater, the room is at $300^o$ K. Assuming the air is described by the equation given above, find the energy density for the two different temperatures. Answer should be in terms of the atmospheric pressure $P_0$, assume it is constant and the room is always at $P_0$.
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22-01-14 10:01:59 |
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[QUE/TH-08006] TH-PROBLEMNode id: 5217page\noindent (a)~ Consider a PV system undergoing change of state from 1 to
2. If the system is in contact with a thermal reservoir at
temperature $T$, show that the maximum amount of work out put
$|W_0|$ is given by
\begin{eqnarray}
|W_0| \le& F_1-F_2&\hfill{[4]}
\end{eqnarray}
\noindent(b)~For a reversible process show that
$$ |W_0| = F_1-F_2 $$
where $F$ is the Helmholtz free energy \hfill{[4]}
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22-01-23 18:01:54 |
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[NOTES/EM-02013] Solid AngleNode id: 5958pageIn this section the concept of solid angle is defined as a generalization of angle in plane geometry
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23-10-12 17:10:14 |
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[2019EM/HMW-02]Node id: 5364pageElectrodynamics Feb 21, 2019
Tut-02
- A line charge carrying a charge \(\lambda\) per unit length and extending from \(-a,0,0\) to \(+a,0,0\) lies along the \(x\)- axis. Find the potential at a point on the \(X\)- axis at point \((d,0,0), d>0\) and at a point \((0,d,0)\) on the \(Y\)-axis.
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22-04-05 16:04:46 |
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[2018EM/HMW-07]Node id: 5428page |
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[NOTES/EM-01005]--Defining the Electric and Magnetic FieldsNode id: 5509pageWe use the Lorentz force on a unit positive charge to define the electric and magnetic fields.
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[1998TH/LNP-22]-Pure SubstancesNode id: 5581page |
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Classical Mechanics --- Notes for Lectures and Problems [CM-MIXED-LOT] Node id: 4687collectionNOTES FOR LECTURES ON CLASSICAL MECHANICS
- NOTES/CM-01 Topics in Newtonian Mechanics
- NOTES/CM-02 Analytical Mechanics
- NOTES/CM-03 Action Principle
- NOTES/CM-04 Hamiltonian Form of Dynamics
- NOTES/CM-05 Spherically Symmetric Potentials
- NOTES/CM-06 Scattering
- NOTES/CM-07 Small Oscillations
- 7.1 Small Oscillations in One Dimension
- 7.2 Small Oscillations
- 7.3 Some Experiments on Small Oscillations
- 7.4 Lagrangian Formualtion of Small Oscillations
- 7.5 A Model of Vibrating Crystals
- NOTES/CM-08 Galilean Transformations, Non Inertial Frames
- 8.1 Rotations about Coordinate Axes
- NOTES/CM-09 Rigid Body Dynamics
- NOTES/CM-10 Canonical Transformations
- LEC/CM08-001 Canonical Transformations
- LEC/CM-08-002
- LEC/CM-08-003
- NOTES/CM-11 Hamilton Jacobi Theory
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[NOTES/EM-03008]-Maxwell's Second Equations from Coulomb's LawNode id: 5645pageMaxwell's equation, \(\nabla \times \vec{E}=0\), can be easily proved by direct computation of curl of electric field of a point charge and appealing to the superposition principle.
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[NOTES/QM-17009] Addition of Angular Momenta Using TablesNode id: 4821page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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qm-lec-17009
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[NOTES/ME-14013]-Angular velocity from rotation matrixNode id: 5705page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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22-08-20 13:08:12 |
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[QUE/SM-08002] SM-PROBLEMNode id: 5074page
- Using \( e(\nu, T) d\nu =\frac{2\pi h}{c^2})\frac{\nu^3}{e^{\beta h \nu}-1}\, d\nu\), where \(e(\nu, T)\) is called the black-body emissivity, show that the energy radiated per unit area and time in the range \(d\lambda\) of \(\lambda\) (where \(\lambda = c/\nu \) is the wavelength) is \[ \left(\frac{2\pi c^2h}{\lambda^5}\right)(e^{\frac{\beta h c }{\lambda}}-1)^{-1} d\lambda \equiv e(\lambda, T) d\lambda.\]
- Show that the wavelength for which \(e(\lambda, T)\) is a maximum is given by \[ \beta h c = 4.965 \lambda_\text{max}\] What does \(\frac{\lambda_\text{max}\nu_{max}}{c}\) equal?
- Solar radiation has a maximum intensity near \(\lambda = 5\times 10^{-5}\)cm. Assuming that the the sun's surface is in thermal equilibrium, determine its temperature.
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