Physics 152 Homework #10

1. Visualizing Avogadro’s Number

Imagine that as a result of a major genetic breakthough, Virginia’s peanut plants become fantastically efficient, producing immense numbers of peanuts at every harvest (although the peanuts are the usual size). The peanuts are shelled, the shells thrown away into the ocean, but after a few harvests the whole state is covered with a layer of shelled peanuts. After some years, the number of peanuts in the layer is equal to the number of molecules in a one liter bottle of air at room temperature and atmospheric pressure. Give a ballpark estimate of the thickness of the layer of peanuts at that time. (Ignore the possible compacting effect of rain, rotting, etc.)

2. In Count Rumford’s account of his cannon-boring experiment, he stated:

“total quantity of ice-cold water which with the heat actually generated by friction, and accumulated in 2 hours 30 minutes, [was] heated [through]180°F, and made to boil, = 26.58lb.”

(The water was absorbing the heat generated by boring the cannon barrel, and was in a wooden sided container for insulation.)

He goes on: “the machinery used in the experiment could easily be carried round by the force of one horse (though, to render the work lighter, two horses were actually employed in doing it).”

Joule actually quotes the data above, then goes on to observe that Watt claimed the power of a horse was 33,000 foot pounds per minute, so you should assume this is the total rate of working of the two horses.

Following Joule, use these data to calculate the number of Joules in one calorie.

3. Are there enough calories in a cheeseburger to get it into low earth orbit (say, 100 miles up)? Check first the potential energy needed, then the kinetic energy.

4. (a) Give rough estimates of the fraction of oxygen molecules in the upper atmosphere that are moving at escape velocity or above. (The temperature can reach 1000K.)

(b) Do the same for any helium atoms in the upper atmosphere.

(c) Do the same for hydrogen molecules.

(d) Mars is at about 0°C. Would you expect it to have any atmosphere? What of the common gases would you expect to find, if any? Give reasons.

(e) We know the Moon has no atmosphere—is that consistent with what we know of its gravity and temperature?

5. Lord Kelvin claimed that when he ran into Joule who was on his honeymoon in Switzerland, Joule was carrying a large thermometer to measure the temperature difference between the top and bottom of a waterfall in a local beauty spot. What do you think Joule would predict the temperature difference between the top and bottom of Niagara Falls to be? (Neglect any possible cooling from evaporation.)