0.7 kg of ice at 0 ◦C and 3 kg of water at Ti are brought into thermal contact in an iso- lated container. All the ice melts, and the mixture reaches an equilibrium temperature of 10 ◦C.

(a) (5 points) Determine the initial temperature Ti of the liquid water.

(b) (1 point) Determine the entropy change ∆S_melt associated with this amount of ice melting.

(c) (3 points) Determine the entropy change ∆S_coolwater associated with the decreasing temperature of the water. (Hint: find an expression for dQ in terms of dT.)

(d) (2 points) Determine the entropy change ∆S_warmwater associated with the increasing temperature of the melted ice.

(e) (2 points) Determine the net entropy change associated with this thermal process. Explain whether your result obeys the Second Law of Thermodynamics.

4. A rocket is nothing more than a fancy tube for carrying fuel and payload—the more fuel/payload, the bigger the tube. Consider a rocket carrying a mass of fuel ?; the mass of the empty rocket plus payload is ? = ?? where ? < 1. The rocket burns its fuel at a rate ?, and the spent fuel is ejected out the back at a speed (relative to the rocket) ?. The rocket blasts off, aimed straight up, and continues to burn as long as it has fuel.

a. Find expressions for the net force on the rocket, its acceleration, velocity, and displacement as functions of time while the rocket is still burning. You may assume gravity is constant (i.e. the displacement is much less than the radius of

the Earth) but you may not assume the mass of the rocket is constant. Remember, F = dp/dt!

Hints:∫ ? ??=?ln(?+??)

and

∫ ln(? + ??) ?? = ? ln(? + ??) + ? ln(? + ??) − ? ?

b. Now take a real rocket, with ?=1.50×107 kg, ?=0.12, ?=9.6×104 kg/s, ? = 1200 m/s. Assuming it launches straight up from the north pole, what is the height and speed of the rocket when its fuel is used up? Is this enough to achieve escape velocity?

Describe how a pn junction is formed

According to quantum electrodynamics, there is a small but finite probability that two photons may scatter against each other. Suppose two photons, with wavelengths λ1 and λ2, collide head-on. Compute the wavelength of one of the photons after the collision, if its scattering angle is θ. (The energy of a photon with wavelength λ is ̄hω, where ω = 2πc/λ.)

A ball of mass 75g is thrown upward with an initial positive velocity, vi, at position A.  

Match the energy transformations taking place for each region of the ball's motion.

Question 23 options:

Name three methods for nanomaterial synthesis. Briefly explain each method. You may use sketches to illustrate your answers.

Find the momentum of a 13.6-MeV gamma ray; a 28-keV X ray; a 4.0-μm infrared photon; a 213-MHz radio-wave photon. Express the momentum in kg · m/s and eV/c.

(a) a 13.6-MeV gamma ray (b) a 28-KeV X ray (c) a 4.0-μm infrared photon (d) a 213-MHz radio-wave photon

How does magnetism work?

1. Calculate the approximate density of nuclear matter in g/cm3 . What would be the diameter of a neutron star with the mass of two solar mass (2M)?

2. Calculate the binding energy of the last neutron in 4He and the last proton in 16O. What does this tell you about the stability of 4He relative to 3He, and of 16O relative to 15N?

Write two sentences or more sentences answering the following. Related to the Palm Springs Wind Farm or any wind farm.

1. Pros and Cons of harvesting wind power.
2. physics principles and parameters involved in harvesting wind power derive the equation for power yielded.

physics

A 49.9- resistor and a 24.7- resistor are connected in series across a 15.2-V battery. What is the voltage across (a) the 49.9- resistor and (b) the 24.7- resistor?

1.To see why the amount of light produced by a black object must only depend on it’s temperature consider the following situation. Suppose you have two black square plates, each at the same temperature, that are placed face to face with a small gap between them. They are both perfectly black and so absorb all electromagnetic radiation incident upon them but suppose one of the plates is emitting twice the radiation of the other. Explain why this would violate the second law of thermodynamics.

1a.For the Rydberg equation for hydrogen, . R_H is the Rydberg constant and is equal to 1.09737 x 10⁷ m^-1.

For the Lyman series, n=1 and the photons are in the ultraviolet. The shortest possible wavelength corresponds to the limit where . What is the photon energy (in eV) of this transition?

1b.What is the energy of the photon in the Lyman series (n=1) corresponding to m = 5? Give your answer in eV.

After the initial cleanup effort at Three Mile Island, approximately 400,000 gallons of radioactive water remained in the basement of the containment building of the Three Mile Island Unit 2 nuclear plant. The principal sources of this radioactivity were Cs-137 at 156 μCi/cm^3 (5.772000 MBq) and Cs-134 at 26 μCi/cm^3 (0.962 MBq). How many atoms per cm^3 of these radionuclides were in the water at that time?

The answer is about 1.78 billion years, but I don't know how to solve for it.

Explain the method of assigning temporal and spatial scales to physical phenomena in fluid
dynamics.