1) For each of the following partial sentences, indicate whether they are correctly completed by the symbol corresponding to the phrase greater than (>), less than (<), or the same as (=).
(a) A chunk of iron is sitting on a table. It is then moved from the table into a bucket of water sitting on the table. The iron now rests on the bottom of the bucket. The force the bucket exerts on the block when the block is sitting on the bottom of the bucket is __________the force that the table exerted on the block when the block was sitting on the table.
(b) A chunk of iron is sitting on a table. It is then moved from the table into a bucket of water sitting on the table. The iron now rests on the bottom of the bucket. The total force on the block when it is sitting on the bottom of the bucket __________ it was on the table.
(c) A chunk of iron is sitting on a table. It is then covered by a bell jar which has a nozzle connected to a vacuum pump. The air is extracted from the bell jar The force the table exerts on the block when the block is sitting in a vacuum is __________the force that the table exerted on the block when the block was sitting in the air.
(d) A chunk of iron is sitting on a scale. The iron and the scale are then both immersed in a large vat of water. After being immersed in the water, the scale reading will be __________the scale reading when they were simply sitting in the air. (Assume the scale would read zero if nothing were sitting on it, even when it is under water.)

2) You and your friends are sitting in an open meadow on a summer day having a picnic. You look up and notice a hot air balloon floating toward you. The balloon is approximately a sphere with a radius of 6 meters and is drifting directly towards you at a speed of about 10 m/s. Hint: The density of normal air is about 1 kg/m3 and the speed of sound in normal air is about 333 m/s (= 1000/3). (a) You guess that the density of the air inside the balloon is 1/2 the density of the air outside the balloon. If that is so, how much does the balloon plus its gondola weigh? (Hint: The density of normal air is about 1 kg/m3.) (b) As the balloon gets closer, you notice that music is coming from a CD player in the balloon's gondola -- Mariah Carey is holding a high note. Your friend who has perfect pitch thought he remembered that it was a C (512 Hz) but he says it sounds a bit off. Why? If the CD is playing a C, what frequency do you hear? Explain.

3) Explain why a helium balloon in a closed automobile moves to the front of the car when the car accelerates, whereas the passengers feel pushed backwards.

4) Suppose you have the following collection of objects: * a pencil, * a coin, * an empty plastic box for cassette tapes with its edges taped shut, * the same box opened up, * a needle, * an unopened can of soda pop, and * an empty can of soda pop. Which of these objects do you expect will float and which will sink on water? Will it make a difference if you carefully place the object with its largest surface on the surface of the water? In which cases? Explain your reasoning. After you have written your answer, perform the experiments and compare your results with your predictions.

5) The density of water is just about 1000 kg/m3. The density of air is just about 1000 times less -- 1 kg/m3 (actually 1.3 kg/m3 at sea level.) From your knowledge of the air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.)

6) Water is poured to the same level in each of the three vessels shown. Each vessel has the same base area. Since the water is to the same depth in each vessel, each will have the same pressure at the bottom. Since the area and pressure is the same, each liquid should exert the same force on the base of the vessel. Yet, if the vessels are weighed, three different values are obtained. (The one in the center clearly holds less liquid than the one at the left, so it will weigh less.) How can you justify this apparent contradiction?

7) In 1654, Otto von Guericke, burgomeister of Magdeburg and inventor of the air pump, gave a demonstration in which two teams of eight horses could not pull apart two brass hemispheres held together only by the pressure of the outside air. The sphere was about the size of a basketball. Estimate the force the teams of horses would have had to exert to pull the hemispheres apart.

8) Two balloons are blown up to different sizes and connected to the opposite sides of a hollow tube. The tube has a valve to prevent air from going from one balloon to the other. The balloons are of different sizes as shown in the figure. When the valve is opened, what will happen? Explain your reasoning. (a) The larger balloon will get smaller and the smaller balloon will get larger until they are of equal size. (b) The smaller balloon will get smaller and the larger balloon will get larger until the smaller balloon is almost gone. (c) Nothing will happen. They will stay the same size.

9) An ideal gas is contained in an airtight box. Complete each of the following five statements below to show the quantitative change that will occur. For example, if you want to say that the volume, initially equal to V, quadruples, complete the statement with "4V".

(a) If the absolute temperature of the gas is halved, the average speed of a gas molecule, v₀, becomes _____.
(b) If the average speed of a gas molecule doubles, the pressure, p, on a the wall of the box becomes _____.
(c) If the absolute temperature of the gas is halved, the pressure, p, on a wall of the box becomes _____.
(d) If the absolute temperature of the gas is increased by 25%, the total internal energy of the gas, U, becomes _____.
(e) If the number of gas molecules inside the box is doubled, but the temperature is kept the same, the pressure, p, on the wall of the box becomes _____.

10) The actual diameter of an atom is about 1 Angstrom (10^-10 m). In order to develop some intuition for the molecular scale of a gas, assume that you are considering a liter of air (mostly N₂ and O₂) at room temperature and a pressure of 105 Pa.

(a) Calculate the number of molecules in the sample of gas.
(b) Estimate the average spacing between the molecules.
(c) Estimate the average speed of a molecule using the Maxwell-Boltzmann distribution.
(d) Suppose that the gas were rescaled upwards so that each atom was the size of a tennis ball (but we don't change the time scale). What would be the average spacing between molecules and the average speed of the molecules in miles/hour?

11) A good student makes the following observation. "If I try to accelerate a small sphere through air, it will be resisted by the air. If I drop an object, it will eventually reach a terminal velocity where the air is resisting as much as gravity is trying to accelerate. The smaller the ball the slower the terminal velocity. But you tell me the Maxwell distribution says that the molecules of air move very rapidly. I estimate that this is much faster than the molecule's terminal velocity, so it can't move that fast. The Maxwell distribution must be wrong."

(a) The Newton drag law for a sphere moving through air is calculated by a molecular model to be |F_{air res}| = 2¼rR²v² where R is the radius of the sphere, r is the density of the air, and v is the velocity of the object through the air. Calculate the terminal velocity for a sphere the size and mass of an air molecule falling through a fluid the density of air (r = 1 kg/m³).
(b) From your estimate in the previous problem, is this speed greater or less than the average speed the molecule should have given the M-B distribution? What is wrong with the student's argument?

12) For each of the following partial sentences, indicate whether they are correctly completed by the word or phrase is greater than (>), is less than (<), or is the same as (=).

(a) An air bubble formed at the bottom of a pan of water increases in size as it rises towards the top surface of the water. As the bubble goes up, the pressure inside the bubble __________ it was on the bottom.
(b) A block of iron is sitting on a table. It is then moved from the table into a bucket of water sitting on the table. The iron now rests on the bottom of the bucket. The total force on the block when it is sitting on the bottom of the bucket __________ it was on the table.
(c) A cube of ice at 0 °C is floating in a dish of water at 0 °C. The internal energy for one gram of the ice __________ the internal energy for one gram of the water.
(d) In a liter of hydrogen (mass = 2 amu) at STP, the number of molecules is __________ the number of molecules in a liter of oxygen (mass = 32 amu) at STP.
(e) In a sample of gas containing hydrogen and oxygen at room temperature, the average velocity of a hydrogen molecule (mass = 2 amu) is __________ the average velocity of an oxygen molecule (mass = 32 amu).

13) Why does Avogadro's hypothesis (that a given volume of gas at a given temperature and pressure has the same number of molecules no matter what kind of gas it is) not hold for liquids and solids?

14) Imagine, as some scientists did in the eighteenth century, that the molecules of a gas occupy fixed positions and are in contact with each other. What conclusions about molecular diameters could you draw (a) from the law of combining volumes and Avogadro's hypothesis and (b) from the ideal gas law?