Directions: Questions 1 and 4 are short free-response questions that require about 20 minutes each to answer and are worth 10 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part.
1.(10 points, suggested time 20 minutes)
Two moles of a monatomic ideal gas are enclosed in a cylinder by a movable piston. The gas is taken through the thermodynamic cycle shown in the figure above. The piston has a cross-sectional area of
i.Calculate the force that the gas exerts on the piston in state A, and explain how the collisions of the gasatoms with the piston allow the gas to exert a force on the piston.
ii.Calculate the temperature of the gas in state B, and indicate the microscopic property of the gas that ischaracterized by the temperature.
i.Predict qualitatively how the internal energy of the gas changes as it is taken from state A to state B.Justify your prediction.
ii.Calculate the energy added to the gas by heating as it is taken from state A to state C along the
(c) Determine the change in the total kinetic energy of the gas atoms as the gas is taken directly from state C to state A.
2. (12 points, suggested time 25 minutes)
A student is given a glass block that has been specially treated so that the path of light can be seen as the light travels through the glass. The student is asked to design an experiment to measure the index of refraction of the glass. The light source available in the laboratory is a hydrogen lamp that emits red light of a known wavelength.
(a) A linear graph is to be used to determine the index of refraction of the glass. Indicate the quantities that should be graphed and describe how the graph could be used to determine the index of refraction of the glass.
(b) Outline an experimental procedure that could gather the necessary data. Include sufficient detail so that another student could follow your procedure. In addition to the glass block and the hydrogen lamp, the equipment in a typical classroom laboratory is available.
(c) Predict how the path of the light will change as it enters the glass. Support your prediction using a qualitative comparison of the speed of light in glass and the speed of light in air.
(d) Describe the process(es) by which red light from the lamp is produced by hydrogen atoms that are initially in the ground state. Draw and label an energy level diagram that supports the atomic process(es) you describe.
3. (12 points, suggested time 25 minutes)
The dots in the figure above represent two identical spheres, X and Y, that are fixed in place with their centers in the plane of the page. Both spheres are charged, and the charge on sphere Y is positive. The lines are isolines of electric potential, also in the plane of the page, with a potential difference of 10V between each set of adjacent lines. The absolute value of the electric potential of the outermost line is 50V.
(a) Indicate the values of the potentials, including the signs, at the labeled points A and B.
Potential at pointA————
Potential at point B————
i. How do the magnitudes and the signs of the charges of the spheres compare? Explain your answer in terms of the isolines of electric potential shown.
ii. The spheres at points X and Y have masses in the same ratio as the magnitudes of their charges. The isolines of gravitational potential for the spheres have shapes similar to those of the isolines shown. Explain why the two sets of isolines have similar shapes.
Let the potentials at the three labeled points be Va, Vb, and Vc. A proton
with charge +q and mass m is released from rest at point B.
(c) Based on your answer to part (b)(ii), briefly describe one similarity and one difference between the electric and gravitational forces exerted on the proton by the system of the two spheres. The similarity and difference you describe must not be ones that generally apply to all forces.
(d) At some time after being released from rest at point B, the proton has moved through a potential difference of magnitude 20V.
i. Determine the change in electric potential energy of the proton-spheres system when the proton has moved through the 20V potential difference. Express your answer symbolically in terms of q,Va,Vb,Vc,and physical constants, as appropriate.
ii. As it moved through the 20V potential difference, the proton was displaced a distance d by the electric force. Determine a symbolic expression for the total work done on the proton by the electric field in terms of the average magnitude Eavg of the electric field over that distance.
iii. Two students are discussing how and why the kinetic energy of the proton would change after it is released.
Student 1 says that if the system is defined as the proton and the spheres, the increase in the proton’s kinetic energy is due to a change in the system’s potential energy as the proton moves through the 20V potential difference.
Student 2 says that if the system is defined as only the proton, the kinetic energy of the proton increases because positive work is done on the proton by the electric field as the proton moves through the 20V potential difference.
Discuss each student’s claims, explaining why each is correct or incorrect.