Electromagnetism - Faraday’s law

A wire is being wound around a rotating wooden cylinder of radius R. One end of the wire is connected to the axis of the cylinder, as shown in the figure. The cylinder is placed in a uniform magnetic field of magnitude B parallel to its axis and rotates at N revolutions per second. What is the potential difference between the open ends of the wire?

A. 0
B. 2πNBR
C. πNBR²
D. BR²/N
E. πNBR³

(GR9677 #47)

Solution:

Faraday's Law: ɛ = − dΦ/dt
with  Φ = NBA  

Given:
N revolution per second
B uniform (constant)
A constant

ɛ = − BA dN/dt
= − BπR²N

|ɛ| = πNBR²

Answer: C

Thermal Physics - Thermal Equilibrium

See Problem #46

In which region are the liquid and the vapor in equilibrium with each other?

A. A
B. B
C. C
D. D
E. E

(GR9277 #47)

Solution:

Region A: V small  → Liquid
Region E: P large, V small → Liquid
Region D and C: V large →  Gas
Phase equilibrium exists only if the temperature of isotherm lies below critical temperature.

Answer: B

Nuclear & Particle Physics - Franck-Hertz Experiment

The Franck-Hertz experiment and related scattering experiments show that

1. electrons are always scattered elastically from atoms
2. electrons are never scattered elastically from atoms
3. electrons of a certain energy range can be scattered inelastically, and the energy lost by electrons is discrete
4. electron always lose the same energy when they are scattered inelastically
5. there is no energy range in which the energy lost by electrons varies continuously

(GR8677 #47)

Solution:

Franck–Hertz experiment: confirmed Bohr's quantized model of the atom by demonstrating that atoms could indeed only absorb (and be excited by) specific amounts of energy (quanta).

Answer: C

Thermal Physics - Entropy

A sealed and thermally insulated container of total volume V is divided into two equal volumes by an impermeable wall. The left half of the container is initially occupied by n moles of a ideal gas at temperature T. Which of the following gives the change in entropy of the system when the wall is suddenly removed and the gas expands to fill the entire volume?

A. 2nR ln 2
B. nR ln 2
C. ½nR ln 2
D. -nR ln 2
E. -2nR ln 2

(GR0177 #47)

Solution:

The container is thermally insulated, dT = 0 or T constant → Isothermal expansion

Entropy for Isothermal expansion: S = Nk ln (V_f / V_i )

Since V_f = 2V_i → S = Nk ln 2 = nR ln 2

Answer: B