1. Two objects are made of the same material, but they have different masses and temperatures. If the objects are brought into thermal contact, which one will have the greater temperature change?
(a) The one with the higher initial temperature
(b) The one with the greater mass
(c) The one with the lesser initial temperature
(d) The one with the lesser mass
2. You hold a piece of wood in one hand and a piece of iron in the other. Both pieces have the same volume, and you hold them fully under water at the same depth. At the moment you let go of them, which one experiences the greater buoyancy force?
(a) The wood does.
(b) The iron does.
(c) Neither; they experience the same buoyancy force.
(d) Not enough information is provided to answer this question.
3. A metal plate has a hole in it with a diameter of exactly 1.0 cm when the plate is at a temperature
T
0. A thin ring of the same metal has an inner diameter of exactly 1.0 cm at the same initial temperature
T
0. When both are heated to
T
= 2T
0, which is true?
(a) The hole in the plate gets smaller, and the opening in the ring gets larger.
(b) The hole in the plate and the opening in the ring get larger.
(c) The hole in the plate and the opening in the ring get smaller.
(d) The opening in the ring gets larger, but we need the relative size of the plate and the hole to know what happens to the hole.
4. Suppose a particular sample of an ideal gas is in a container with a volume of 2m
3
at a temperature of 350 K, at the surface of the Earth. How many moles of this gas must be present if the
net
force on the container walls is to be zero? (a) 0 moles
(b) 6.9 × 10−4
moles
(c) 69 moles
(d) Not enough information is provided to answer this question.
5. In question 6 in the next part, viscosity is ignored. How would including viscosity change your results?
(a) Viscosity impedes motion, and the pump gauge pressure would increase.
(b) Viscosity impedes motion, and the pump gauge pressure would decrease.
(c) Viscosity propels motion, and the pump gauge pressure would increase.
(d) Viscosity propels motion, and the pump gauge pressure would decrease.
6. A large cylindrical tank with diameter
D
is open to the air at the top. The tank contains water to a height
H. A small circular hole with diameter is then opened at the bottom of the tank. Ignore any viscosity effects.
(a) Find the height
y
of water in the tank as a function of time
t
after the hole is opened.
(b) If the initial height
H
of the water is doubled, by what factor does the time it takes to completely drain the tank increase?
7. Your misguided physics professor proposes a new temperature scale (the bohn scale) given in
◦B. He wants to define 0.0
◦B as the normal melting point of boron and 100.0
◦B to be the normal boiling point of boron. (Feel free to look up those temperatures.) At what temperature does water boil on the bohn scale?
8. What thermal volumetric contraction (expressed as a fraction of the original volume) of 1.7 kg of carbon disulfide releases enough energy to fully melt 1.7 kg of ice originally at 0
◦C? (Feel free to look up the relevant properties of these substances.)
9. Suppose 11 gas molecules have speeds evenly distributed between 500 m/s and 1500 m/s(inclusive) in increments of 100 m/s.
(a) What is the average speed of these molecules?
(b) What is the
rms
speed of these molecules?
(c) What is the temperature of this gas sample, if the molar mass of thisgas is 35 × 10−3
kg/mol?
10. Suppose a vertical pipe is to be used as part of a system to manually cycle nutrients upward from the floor of a lake. (Many lakes do this naturally, some do not. Green Lake, near Syracuse, NY, is one such lake.) A pump is to be installed on the lake floor at the base of the pipe. The base of the pipe will have a diameter of 9 cm. The nozzle of the pipe at the top will have a diameter of 4 cm. The lake is 59 m deep at the installation point. (Ignore any viscosity.)
SCENARIO A.
(a) What is the absolute pressure at the pump depth?
(b) What is the absolute pressure at the surface of the lake?
(c) What is the ratio of the flow speed at the pump to that at the nozzle?
(d) The design for the installation calls for propelling the water out of thenozzle 3 m into the air as a fountain. What gauge pressure in the pipe at the pump is required for this?
SCENARIO B.
(e) When the air temperature is 0
◦C, the water at the surface freezes to form a sheet of ice. Explain why the entire volume of the lake doesn’t freeze.
(f) Write an equation that expresses the heat current
H
of conduction through the ice as a function of the thickness
h
of the ice sheet (of area
A) already formed. Assume the air temperature is a constant -10
◦C, and that the temperature of the bottom of the ice sheet is 0
◦C.
(g) Since , use your answer to (f) to express the amount of heat
dQ
conducted through the ice sheet in time
dt.
(h) Consider a short time interval
dt, and let an additional thickness
dh
be formed in that time. Express the mass
dm
that freezes during this time in terms of
dh, the area
A, and the density of water.
(i) Express the amount of heat
dQ
that must be removed from the water at the bottom of the ice sheet to freeze the mass
dm
you found in (g).
(j) Based on (g) and (i), set the expressions for
dQ
equal to each other to obtain a differential equation relating the heat that must be removed to freeze a new layer to the heat conducted through the ice sheet.
(k) Separate variables, and integrate to find the thickness
h
of the ice sheet as a function of time
t. (Note that
h
= 0 when
t
= 0.)
(l) Use your answer to (j) to calculate how long it will take to form an icelayer 20 cm thick.
(m) Use your answer to (j) to calculate how long it will take for the entire 59 m of the lake to freeze.
(n) Is it likely that the entire lake freezes? Explain.
11. You have two identical containers, one containing gas A and the other containing gasB. Both gases are under the same pressure and are at 5.0
◦C. The molecular masses are
mA
= 3.29 × 10−27
kg and
mB
= 6.12 × 10−26
kg.
(a) Which gas has greater translational kinetic energy per molecule?
(b) Which gas has greater
rms
speed?
(c) Assuming you can only change one of the containers, the temperature ofwhich gas should be raised so that both gases will have the same
rms
speed?
(d) What temperature will do the job in (c)?
(e) Now that the molecules of the two gases have the same
rms
speed, which gas’s molecules have greater average kinetic energy?
(f) Suppose that instead of changing only one in (c), you could changeboth; the energy to raise the temperature of one of the gases will be removed from the other, both in constant-volume processes. In terms of the molar heat capacities of these gases at constant volume,
CA
and
CB
, express the ratio of the final temperature
TA
of gas A to that of gas B
TB
such that the
rms
speeds are again the same.