1. Radioactive element X has a half-life of approximately 50 days. Radioactive element Y has a half-life of approximately 100 days.A 0.8 g sample of element X and a 0.8 g sample of element Y are weighed and examined. Some time later, both samples are measured again and 0.2 g of element X remains. How much of element Y remains?
(A) 0.1 g
(B) 0.2 g
(C) 0.4 g
(D) 0.8 g
2. A sample of a gas is in a container with a movable piston. Only one action is performed to take the gas from state A to state B via the process shown in the above graph of pressure as a function of volume. Which of the following could be the one action?
(A) Gas molecules were removed from the container.
(B) Thermal energy was added to the gas.
(C) The piston was pulled out.
(D) The gas was allowed to freely expand.
3. The graph above shows the electric field E of an electromagnetic wave as a function of position x at a particular instant. Which of the following equations, where all quantities are assumed to have units consistent with the graph, best represents the graph?
(A) E = 10 cos(2πx/10)
(B) E = 10 cos(2πx/5)
(C) E = 5 cos(2πx/10)
(D) E = 5 cos(2πx/5)
4. Some students observe that a hollow metal sphere hanging on an insulating string is attracted to a positively charged rod. They decide that this is evidence that the sphere could also be charged. The answer to which of the following questions might determine whether they are correct?
(A) Is the sphere still attracted when the positively charged rod is placed on the other side of the sphere?
(B) Is the sphere repelled by a negatively charged rod?
(C) Is the attraction of the sphere to the rod weaker when the distance between them is increased?
(D) Is the attraction of the sphere to the rod stronger when the charge on the rod is doubled?
5. Two identical containers, X and Y, each contain one mole of an ideal monatomic gas. The atoms in container X have a higher average kinetic energy than those in container Y. The containers are thermally insulated from the external environment and placed into thermal contact with each other at time t = 0 . Which of the following accurately describes the interactions between containers X and Y ?
(A) The net result is that energy is transferred from container X to container Y.
(B) The amount of energy transferred between the containers depends on the type of atoms each contains.
(C) After equilibrium is reached, the atoms in container X will still have a different average kinetic energy than those in container Y.
(D) All the atoms in container X slow down, and all the atoms in container Y speed up.
1. (10 points, suggested time 20 minutes)
A group of students is asked to design a heater for an indoor swimming pool using an electrically insulated current-carrying wire. The energy from the wire heats the water. The heater should deliver 10 kW of power to the water in the pool.
(a) The students use wire that has a cross-sectional area of 1.3 × 10-5 m2 and a resistivity of 3.0 × 10-6 Ω•m . They have access to a 240 V power supply. Calculate the length of the wire needed to construct the heater.
(b) The wire is completely submerged in the water, and the heater is turned on. After a while, both the water and the air above it are noticeably warmer.
i. Identify and describe both the primary process that transfers energy through the wire’s electrical insulation and the primary process that transfers energy through the water.
Electrical Insulation Water
ii. The door to the pool area is open, and the air outside is colder than the air in the pool area. The heater must remain on to maintain a constant water temperature that is greater than the air temperature in the pool area. Explain how the first and second laws of thermodynamics can be applied to show that this must occur.
The door to the pool area is then closed so that energy transfer and air transfer into and out of the area are negligible. After some time the air in the pool area becomes warmer.
(c) On the graph below, sketch the thermodynamic process that the air in the pool area undergoes as it becomes warmer. Compare the amount Q of energy transferred to the air by heating to the change △U in the air’s internal energy.
(d) When the temperature of the room is 276 K , the air pressure is 1.0 ×105 Pa. Calculate the force exerted by the air in the room on a door that measures 2.0 m by 0.90 m when the temperature of the room is 310 K .
2. (12 points, suggested time 25 minutes)
Students use a lightbulb, a screen, and a meterstick to determine the focal length of a concave mirror from a graph.
i. Describe a procedure that could be used to collect appropriate data and the measurements to be taken.
ii. Describe how the focal length can be determined from the graph.
(b) The figure below represents one arrangement of a concave mirror and an object. The dot represents the focal point of the mirror and the arrow represents the object. Draw a ray diagram to illustrate the formation of the image that includes at least two rays and the resulting image.
(c) Some students take the concave mirror outside and hold it with the concave side facing the Sun. The students want to locate the image of the Sun. They measure the temperature of the air in front of the mirror along the principal axis and graph the air temperature as a function of distance from the mirror. The graph below is their best-fit curve to the data.
i. Based on the curve, at what distance from the mirror would you expect to find the image of the Sun?
ii. Use a relevant equation to explain how your response to (c)(i) relates to the focal length of the mirror.