Thermal Physics - Laws of Thermodynamics

An experimenter needs to heat a small sample to 900 K, but the only available oven has a maximum temperature of 600 K. Could the experimenter heat the sample to 900 K by using a large lens to concentrate the radiation from the oven onto the sample as shown above?

A. Yes if the volume of the oven is at least 3/2 the volume of the sample.
B. Yes, if the area of the front of the oven is at least 3/2 the area of the front of the sample.
C. Yes, if the sample is placed at the focal point of the lens.
D. No, because it would violate the conservation of energy.
E. No, because it would violate the second law of thermodynamics.

(GR9677 #91)

Solution:

The second law of thermodynamics:
No process is possible whose sole result is the transfer of heat from a colder to a hotter body.

The oven can only heat the sample to a maximum of 600 K without violating the Second Law.

Answer: E

Nuclear & Particle Physics - Weak Interaction

The particle decay must be a weak interaction because

A. the is a lepton
B. the has spin zero
C. no neutrino is produced in the decay
D. it does not conserve angular momentum
E. it does not conserve strangeness

(GR9277 #91)

Solution:

Weak interactions:

• affect all known fermions (leptons and quarks; spin is a half-integer) caused by the emission or absorption of W and Z bosons. 
• the only process in which a quark can change to another quark, or a lepton to another lepton (flavor changes).
• fails to conserve strangeness or parity. 
• interactions involving neutrinos are mediated by the weak interaction.

A and B FALSE.

• Weak interaction changes lepton to another lepton.
• If is a lepton should be lepton too.
• According to B, has spin zero, means is a boson and does not interact mediated by weak interaction.

C FALSE.

• The neutrino is a fermion and interact primarily through the weak force.

D FALSE.

• Conservation of angular momentum is an exact laws, or more precisely have never been shown to be violated

Answer: E

Nuclear & Particle Physics - Bragg Diffraction

When a narrow beam of monoenergetic electrons impinges on the surface of a single metal crystal at an angle of 30 degrees with the plane of the surface, first-order reflection is observed. If the spacing of the reflecting crystal planes is know from x-rays measurements to be 3 Angstrom, the speed of the electron is most nearly

A. 1.4  × 10⁻⁴ m/s
B. 2.4 m/s
C. 5.0  × 10³ m/s
D. 2.4  × 10⁶ m/s
E. 4.5  × 10⁹ m/s

(GR8677 #91)

Solution:

Bragg's Law: nλ = 2d sin θ 

De Broglie wavelength: λ = h/m_ev

h/m_ev = 2d sin θ / n
v = nh / (2m_ed sin θ)

Given:
n = 1 (first-order reflection)
d = 3 Angstrom = 3 × 10⁻¹⁰ m
θ = 30 →  sin 30 = 0.5
m_e =  9.11 × 10^{−31 kg}
h = 6.63 × 10⁻³⁴ Js

v = (6.63 × 10⁻³⁴)/[2( 9.11 × 10⁻³¹)(3 × 10⁻¹⁰)(0.5)]
= [6.63/(9.11 × 3)] × 10⁻³⁴ × 10⁴¹
= [2/(3 × 3)] × 10⁷ ≈ 0.22 × 10⁷ = 2.2 × 10⁶ m/s  

Answer: D

Classical Mechanics - Rotational Motion

The cylinder shown above, with mass M and radius R, has a radially dependent density. The cylinder starts from from rest and rolls without slipping down an inclined plane of height H. At the bottom of the plane its translational speed is (8gH/7)^{1/2. Which of the following is the rotational inertia of the cylinder?}

(GR0177 #91)

Solution:

Initally, it starts from rest, from height H,



At the bottom of the plane,



Conservation of Energy,



with and



Answer: B