Browse & Filter

Ten grams of water at 20$^\circ$C is converted into ice at
-10$^\circ$C at constant atmospheric pressure. Assuming the heat
capacity per gram of liquid water to remain constant at 4.2 J/g\,K,
and that of ice to be one half of this value, and taking the heat of
fusion of ice at 0$^\circ$C to be 335 J/g, calculate the total
entropy change of the system.

Electrodynamics                                                Apr 8, 2019
                                        Quiz-X

• At the upper surface of the Earth’s atmosphere, the time-averaged magnitude of the Poynting vector \(<S> =1.35^10^{W/m}^2\) is referred to as

  the solar constant.

  1. Assuming that the Sun’s electromagnetic radiation is a plane sinusoidal wave, what are the magnitudes of the electric and magnetic fields?
  2. What is the total time-averaged power radiated by the Sun? The mean Sun-Earth distance is \(R =1.50\times10^{11}\) m .

• Following equation contains the complete information about the electromagnetic wave \begin{equation*} \vec{E}(z,t)=E_0\sin(kz-\omega t)\hat{i} \end{equation*} Find the directions of wave propagation, wavelength, frequency, speed of propagation, magnetic field, the Potynting vector and the intensity of the wave.

The parabola method was used to measure charge to mass ratio of the electron by measuring the deflection of the electrons when they pass through a uniform electric field. The method is described here and an expression for \(e/m\) in terms of the deflection of the electron. 

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Assuming time development of states to be given by  \[i\hbar \dd[\ket{\psi, t}]{t} = H \ket{\psi t}, \] an equation for time variation of average value of a dynamical variable is derived. Classical correspondence  is used to identify the generator of time evolution with Hamiltonian. A dynamical variable not depending explicitly on time is a constant of motion if it commutes with the Hamiltonian.

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qm-lec-17005

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Consider 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