A mass of 3 kg of water at 50oC has been heated to vapour at a temperature of 125oC in an oven. The specific heat capacities for water in the form of liquid (Cw), solid (Cice) and gas (Cv) are 4.187 kJ.kg-1.K-1, 2.108 kJ.kg-1.K-1, and 1.996 kJ.kg-1.K-1, respectively. Also, latent heats of fusion and vaporization are given as 3.33 x 105 J.kg-1 and 2.22 x 103 J.kg-1, respectively. NB: Number your answers correctly!

(a) What would be the entropy of water in the form of liquid, SL? (5)

(b) Calculate the entropy of the system when it changes its state/phase to vapour, Sv. (3)

(c) Compute the total entropy, STotal, of water between 50 oC and 125 oC. (5)

1.For an angle of zero between the magnetic field and the vector normal to the plane of the coil: (a) What happens to the light bulb as it enters the magnetic field region? Explain. (b) What happens to the light bulb as it moves while it is completely inside the magnetic field? Explain. (c) What happens to the light bulb as it exits the magnetic field region? NOTE: Use Faraday’s Law to explain.

2.For an angle of zero between the magnetic field and the vector normal to the plane of the coil: What happens to the light bulb when the you flip the direction of the magnetic field? Explain using Faraday’s Law.

3.For an angle of zero between the magnetic field and the vector normal to the plane of the coil: What happens to the light bulb when the magnitude of the magnetic field varies? Explain using Faraday’s Law

4.For an angle of zero between the magnetic field and the vector normal to the plane of the coil: What happens to the light bulb when the coil moves vertically? Explain using Faraday’s Law

fred places two circular loops of conducting wire, one large (radius R) and one small (radius r),
on a horizontal table such that they are centred at the same point. He arranges the larger loop
to carry a constant current I clockwise (when viewed from above). In order to induce a current
in the smaller loop, fred then lifts the smaller loop vertically upwards at a constant speed v,
without changing its orientation.
1 - Explain why fred is correct to expect an induced current in the smaller loop, and determine which way this current will flow.
2 - Show that the emf induced in the small loop is approximately
E = (U_03IR^2v/2z^4)*PIr^2
where z is the height above the table. You may use the result that the magnetic field
along the z-axis produced by the large loop is B = µ_0IR^2/2z^3. Make sure to explain,
with the aid of a diagram, the simplifying assumptions you need to make.
3 - Meanwhile sam, who is also in the room, happens to be levitating upwards at the same
velocity as the small loop. Thus the small loop is stationary in her frame. Explain,
from sam’s point of view, why she should also expect to see an induced emf in the small
loop. Your explanation should comment on the differences between fred’s and sam’s
description of the cause of the emf and explain how it is that they can both be correct.

Compare and contrast the four-planet detection techniques described during lectures. Use labelled diagrams and equations relevant to each technique to illustrate and support your statements. The methods are: Transit detection, Radial velocity method, direct imaging and microlensing

1. A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s. Find the magnitude and the direction of the velocity of the system Immediately after the collision.

2. In an elastic collision of two objects,

a. momentum is not conserved.

b. momentum is conserved, and the kinetic energy after the collision is less than its value before the collision.

c. momentum is conserved, and the kinetic energy after the collision is the same as the kinetic energy before the collision

d. the kinetic energy of the system after the collision depends on the masses of the objects

3. Object 1 has more kinetic energy than Object 2. How do the magnitudes of their momenta compare?

a. P1=P2

b. P1>P2

c. p1 ≥ p2

d. not enough information given to tell

4. Explain the processes of lasing in the Co2 laser. What is the function of Nitrogen, and Helium in the gas mixture of the co2 laser?

(a) Compute the first-order correction to all energy eigenvalues of a particle in a square well in the region 0 ≤ ? ≤ L with added potential: ?(?) = ?_o? when 0 ≤ ? ≤ L/2 and ?_o (L − ?) when L/2 ≤ ? ≤ L.

(b) Using the given potential, use the variational theorem to compute an upper bound to the ground state using the trial function below

∅(?) = ?₁ (2/L)^1/2 sin ( ??/L ) + ?₂ (2/L)^1/2 sin ( 2??/L )

A sphere with radius a = 8 cm is in a conductive sphere shell with an internal radius of b = 12 cm and an outer radius of c = 18 cm with a load of -200 mC.
a) Determine the load distribution in the sphere and sphere shell.
b) Calculate the value of the electric field in r = 0 cm, r = 4 cm, r = 8 cm, r = 10 cm, r = 14 cm, r = 18 cm and r = 50 cm, and plot the electric field with respect to r.

A 2500-kg rocket blasts off from Planet A headed directly towards Planet B. The masses of Planet A and B are 6x1024 kg and 3x1025 kg respectively and the distance between the planets is 4x108 m. How far from Planet A will the rocket have traveled when the net gravitational force on the rocket from the two planets is zero?

For Astronomy class, please answer this question clearly, thank you.

Describe the similarities and the differences between the mechanisms by which Terrestrial and Jovian planets generate their magnetic fields.

A uniformly charged disk of radius 35.0 cm carries a charge density of 6.40 ✕ 10^-3 C/m². Calculate the electric field on the axis of the disk at the following distances from the center of the disk.

(a) 5.00 cm
MN/C

(b) 10.0 cm
MN/C

(c) 50.0 cm
MN/C

(d) 200 cm
MN/C

An engine that operates by means of an ideal diatomic ideal gas in a piston with 2.70 moles of gas. The gas starts at point A with 3x103 Pa of pressure and 2.5x10-2 m3. To get from B from A, it is expanded by an isobaric process to double the initial volume. From B to C it expands adiabatically until it reaches three times the volume in A. From C to D the pressure decreases without changing the volume and from D to A it is an isothermal compression. a) Draw the PV diagram of the process and determine the pressure and volume at each vertex. Calculate: b) full cycle work. C) The heat transferred in each process. D) The real efficiency and efficiency of carnot. D) The change of entropy in each process.

Forgive me, I'm a little bit vague on the detail.

If the projectile rebounds upon impact instead of sticking to the pendulum, how would the vertical rise of the pendulum compare to the value obtained when the two move together? Give an explanation.

Describe in detail, with sketches as appropriate, the requirements for a setup of a mechanical experiment that allows to measure the weight of individual atoms. Provide details of a sensor (eg. scale, mass), the sensor actuation and the sensor read-out (eg. experimental noise, physical principle). How do you prove that the measured atomic mass stems specifically from the atoms you analyse? (Consider environmental sources of measurement noise)

This question featured in an Oscillations section of a past exam paper. Any help greatly appreciated! Thanks.

Thermodynamics and Statistical Mechanics problem:

(a) Derive the Maxwell speed distributions in one and two dimensions.

(b) What is most likely speed in each case?

(c) What is average speed in each case?

(d) What is root-mean-square speed in each case?