2. The heat capacity of one mole of aluminum at low temperature (below 50 K) follows the form

CV = aT+bT³

where a = 0.00135 J/K² and b = 2.48×10^-5 J/K⁴. (The first term comes from the free electrons and the second term is due to lattice vibrations.) Use this expression to derive a formula for the molar entropy of aluminum as a function of temperature, assuming that the entropy at 0 K is zero. Finally, determine the ratio of the multiplicity of a mole of aluminum at 10 K to its value at 1 K.

3. In order to take a nice warm bath, you mix 50 liters of hot water at 55 ◦C with 25 liters of cold water at 10 ◦C. Assume that the tub is insulated fiberglass that thermally isolates the water. You can also assume that the mixing happens quickly enough that energy is not lost to the air through the open surface of the water.

(a) How much heat is involved in warming the water?

(b) How much entropy did you create?

why orthogonal components are useful for science?

Charge q = + 15 nC is uniformly distributed on a spherical shell that has a radius of 120 mm.

1. What is the magnitude of the electric field just outside the shell? (Express your answer with the appropriate units.)

2. What is the magnitude of the electric field just inside the shell? (Express your answer with the appropriate units.)

3. What is the direction of the electric field just outside and just inside the shell?

4. What is the electrostatic potential just outside the shell, relative to zero at infinity? (Express your answer with the appropriate units.)

5. What is the electrostatic potential just inside the shell, relative to zero at infinity? (Express your answer with the appropriate units.)

6. What is the electrostatic potential at the shell's center? (Express your answer with the appropriate units.)

7. What is the electric field magnitude at the shell's center? (Express your answer with the appropriate units.)

In this experiment, we have claimed to measure the speed of sound in air. To do this, we have used an audible frequency sweep. Why can we claim that the speed of sound will be the same over the bandwidth of the sweep? Is this assertion justified based on your results from experiment 2? Hint: Consider how sound (longitudinal pressure waves) propagate in a medium. (5 pts)

A woman of mass m = 58.9 kg sits on the left end of a seesaw—a plank of length L = 4.04 m, pivoted in the middle.

(a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M = 69.9 kg sit if the system (seesaw plus man and woman) is to be balanced?
1.702m (Correct)

(b) Find the normal force exerted by the pivot if the plank has a mass of m_pl = 12.8 kg.
1387.68N (Correct)

(c) Repeat part (a), but this time compute the torques about an axis through the left end of the plank.
1.65m (Correct)

QUESTION: Suppose a 27.8-kg child sits 0.73 m to the left of center on the same seesaw as the problem you just solved in the PRACTICE IT section. A second child sits at the end on the opposite side, and the system is balanced.

(a) Find the mass of the second child 10.05 kg?

(b) Find the normal force acting at the pivot point.____N?

Consider a conducting sphere of radius R carrying a net charge Q.

a). Using Gauss’s law in integral form and the equation |E| = σ/ε₀ for conductors, nd the surface charge density on the sphere. Does your answer match what you expect? b). What is the electrostatic self energy of this sphere?
c). Assuming the sphere has a uniform density ρ, what is the gravitational self energy of the sphere? (That is, what amount of gravitational energy is required/released when the sphere is assembled.) d). Assuming Q = 1 C and the sphere is made of ironρ M = 7870 kg/m3, is there a radius R such that the gravitationalself-energy is just enough to overcome the electrostatic self energy? If so, nd R.

Your little dog, Fluffy, is excited to see you and jumps straight up in the air to a height of 0.680 m . What is Fluffy's initial speed as she leaves the ground? You can assume that Fluffy is in "Free Fall" (constant acceleration) during the jump.

Correct

Part B

What is the length of time that Fluffy is in the air?

Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p

(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V ]

(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]

(c) Give a physical explanation for the difference between the two.

(Note: Since the mole number n is just the particle number N divided by Avogadro’s number, holding one constant is equivalent to holding the other constant.)

A basketball player grabbing a rebound jumps 78 cm vertically. How much total time (ascent and descent) does the player spend (a) in the top 12 cm of this jump and (b) in the bottom 12 cm? Do your results explain why such players seem to hang in the air at the top of a jump?

An unknown positive point charge is placed at x = -0.27 m, y = 0 m, a charge of -2.8 micro-coulombs is placed at x = 0 m, y = -0.20 m, a charge of +2.2 micro-coulombs is placed at x = +0.50 m, y = -0.29 m, and charge of +2.8 micro-coulombs is placed at x = 0 m, y = +0.20 m. If the total electric field due to all four charges at the origin is 4.5 x 106 N/C (the x component of the total electric field is positive), what is value of the magnitude of the unknown charge in micro-coulombs? If negative, include a negative sign.

Point charges of 6.75 µC and

−4.00 µC

are placed 0.300 m apart. (Assume the negative charge is located to the right of the positive charge. Include the sign of the value in your answers.)

(a) Where can a third charge be placed so that the net force on it is zero?
m to the right of the

−4.00 µC

charge

(b) What if both charges are positive?
m to the right of the  4.00 µC charge

1. What is light? 2. What are the three models of light? 3. When is each model of light applicable? 4. What is visible light? 5. What is white light? 2-3 sentences each.

A person measures her heart rate by counting the number of beats in 30 s. If 42 ± 1 beats are counted in 30.0 ± 0.5 s, what is the heart rate and its uncertainty in beats per minute?

A 2100-m-high mountain is located on the equator.

How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth's radius is 6400 km.

Express your answer to two significant figures and include the appropriate units.

When the police want to know how fast your car is going, they shoot a "radar gun" at the car. The radar gun emits waves at approximately 24.15 GHz. Those waves reflect off of your car and are detected by the same "radar gun" that emitted them. The detector can detect both frequency and intensity. Using concepts of general physics, explain how the radar gun works. You probably want to draw pictures, use an equation or two, and use words.