< Physics 201 MWF10:20 Fall 1998 (Ford)

Exam IV Chapts. 12--15 in Cutnell and Johnson, 4th ed.


(18 pts) 1. A metal can is filled to the brim with 6.0 × 10^-4 m³ of water at 20 °C. When the can and the water are both heated to 75 °C, 5.0 × 10^-6 m³ of water spills. The coefficient of volume expansion of water is 2.07 × 10^-4 (C°)^-1). What is the coefficient of volume expansion of the metal can?

Ans.__5.55 × 10^-5 (C°)^-1___


(20 pts) 2. A mass m of ice at -20.0 °C is added to 1.5 kg of water that is initially at 90.0 °C. What must be the mass m of the ice if the final temperature of the system is to be 40.0 °C? Assume no heat is lost to the surroundings. (Note: Tables of specific heat capacities and latent heats are given on the formula sheet.)

Ans. __0.579 kg__


(22 pts) 3. In an aluminum pot, 0.80 kg of water at 100 °C boils away in five minutes. The bottom of the pot is 3.0 × 10^-3 m thick and has a surface area of 0.020 m². To prevent the water from boiling too rapidly, a brass plate has been placed between the pot and the heating element. The plate is 1.5 × 10^-3 m thick, and its area matches that of the pot. The thermal conductivity of aluminum is 240 J/(s·m·C°) and the thermal conductivity of brass is 110 J/(s·m·C°). Assuming that heat is conducted into the water only through the bottom of the pot and that no heat is lost to the surroundings, find

a) the temperature of the interface between the aluminum and the brass

Ans. ___103.8°C___

b) the temperature of the bottom of the brass plate, where it is in contact with the heating element

Ans.__107.9°C__


(18 pts) 4. A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In five minutes of operation of the engine, the heat rejected by the engine melts 0.040 kg of ice. During this time, how much work W is performed by the engine?

Ans.___4.91 × 10³ J___


(22 pts) 5. Two moles of a monatomic ideal gas (C_V = 3R/2) undergoes the two processes shown in the sketch. Process A to B is at constant pressure and process B to C is at constant volume. The temperatures of the states A, B, and C are given. For each process, calculate U, Q, and W. (Note: R = 8.31 J/(mol·K).)

process A to B

Ans. U =___4986 J___

   Q = ___8310 J___

   W = ___3324 J__

process B to C

Ans. U =___-4986 J___

   Q = ____-4986 J___

   W = ____0____