One advantage to being small is that it is easier to cool off after exertion than if you are large. For example, hummingbirds generate a lot of heat as their wings beat quickly, but they can cool off very quickly in response. (The flip side is, it is harder to stay warm when the air temperature is low.) In this problem we will develop a simple model of the smallest shrew and a polar bear cooling off. We will model both mammals as spheres (Volume = 43?r3 ; surface area = 4?r2 ) with a 0.50 cm barrier of air next to their skin (k= .026 W/(mK)). In both cases we will take the internal temperature to be 40 degrees C, and the outside temperature to be 22 degrees C. The shrew has a radius of 0.0175 m, while the polar bear has a radius of 1.5 m

Part A. What is the rate of heat loss through conduction for the shrew? Give all answers in this question to three sig figs.

Part B. What is the rate of heat loss through conduction for the bear?

Part C. Let's assume that the shrew needs to loose 100J of thermal energy in order to cool off to a safer internal temperature. We want to find out how much thermal energy the bear needs to loose. We will do this by assuming that the amount of thermal energy each has to loose is proportional to their volume: Thermal needed to loose = Constant * Volume of mammal and that the constant is the same for both the shrew and the bear. There are two ways (at least) to solve this. One is to find the value of the constant for shrew and use that value for the bear. The other is to use proportions, knowing that the constant is the same for both mammals.

Part D. How long will it take the shrew to loose this 100 J of heat through conduction? Hint: if the rate of heat loss via conduction were 50 Watts, the shrew would be losing 50 Joules every second (Watt=Joule/second), so it would take 2 seconds to cool off.

Part E. How long would it take the bear to cool off?

You observe two point sources of light that are spaced 5 cm apart which are each emitting light of wavelength of 420 nm. If the diameter of your pupil is 2 mm, how distant can the objects be from your eye for you to just barely resolve them?

A long, straight wire carries a steady current of 50 A. What is the magnetic field strength at a distance of 7 cm from the wire?

Find an example of a reverse salient from the past 75 years.

Describe the full system that contains the reverse salient, the reverse salient itself, explaining why it was a reverse salient, and the technological advance that made the reverse salient obsolete in the system.

Note: If the reverse salient is still a problem, describe the work being done to overcome the problem.

Explain the continuity equation for electric current and how does divergence apply for electric current? What is the relaxation time of a material?

Imagine two carts with different masses colliding (m1 = 2.0 kg, m2 = 1.0 kg). If cart one is initially moving at 10 m/s and the other cart is stationary, calculate the final speed of each mass after they have a 100% elastic collision. Please show all work!

Show the cleavages and permissible transitions of the sodium atom D₁( ²P_1/2 ---> ²S_1/2 ) and D₂ ( ²P_3/2 ---> ²S_1/2 ) lines in a strong ( B_out > B_in ) magnetic field in the energy diagram.

What is the image distance when d0 =10.11 cm, f = 3.0 cm, di = ?

. Write down the lens formula (1/f = 1/o + 1/i)

. What happens in the simulation experiment when you change the focal length?

. What happens to the image if you change the object distance?

Describe the ray tracing - light tracing for the following:

. A Refracting telescope

. A Reflecting telescope

. A pair of binoculars. Porro Prism and Roof Prism binoculars.

. A microscope

. What happens to the image if you change the object size?

. Write down the Lens Maker's equation and explain

1/f = (n - 1 ) ( 1/R1 - 1/R2)

Explain the strengths and weaknesses of the Bohr model.

1. Show three possible 3p → 2s (6x1014 s^-1 frequency) transition for each case of including spin in strong magnetic field and not including spin in strong magnetic field.
2. If µB = 0,4 eV, find the frequency of transition from 3p (m₁,m₂) = (1,1/2) to 2s (m₁,m₂) = (0, 1/2) in previous question’s transition.

A gas undergoes an isothermal expansion from V1=1.4L followed by isobaric compression, p=cst. if p1=4.4atm, p2=2.2atm→?Nm2, calculate the total work done by the gas.
Hint:
W=∫dW=∫pdV=∫nRTVdV

Assume Silicon (bandgap 1.12 eV) at room temperature (300 K) with the Fermi level located exactly in the middle of the bandgap. Answer the following questions.

a) What is the probability that a state located at the bottom of the conduction band is filled?

b) What is the probability that a state located at the top of the valence band is empty?

1. An explanation of the relevant symmetry.

2. An explanation of your choice of the Gaussian surface and how that choice arises out of the symmetry of the charge distribution.

3. A calculation along with a neat figure showing the charge distribution, the Gaussian surface, and the electric field vector and the area vector for a general area element.

which of the following correctly reflect ways in which a chemical equilibrum can be shifted? changing the temperature of the system, changing the concentration of reactants or products, changing the pressure of a gaseous reactants, changing the volume of a container for an aqueous reaction

For each of the following, put "A" if it is always true, "S" if it is sometimes true, or "N" if it is never true.

(a) The net force on an object is zero if its speed remains constant.

(b) Normal force cannot do work on any system.

(c) If mechanical energy is not conserved, friction is the reason.

(d) A person riding a ferris wheel will feel heaviest at the bottom.

(e) If a moving object changes direction, a net force must act on it.

(f) The terminal velocity of a 25 kg object is higher than that of a 10 kg object.