# Physics H133: Problem Set #14

Here are some hints, suggestions, and comments on the problem set.
## Two-Minute Problems

Remember to give a **good** explanation, no longer than
two sentences.

- T2T.7: For each of the 4 questions, select A,B,C, or D and give a
short explanation of your choice. How are K, v, U, P related
to T, numbers of particles, their masses, etc.?
- T2S.3: (a) What would happen if the average velocity of
the molecules were not zero? (b) How is the rms speed defined? What is
the difference between speed and velocity?
- T3T.4: Is the gas expanding or contracting? What is the work done
on the gas? Is the temperature changing? What does this imply
for the change in thermal energy? What does the first law
of thermodynamics say?
- T3T.8: Review the section on Adiabatic Processes. How do the volume
and pressure ratios between initial and final state relate
to each other?

## Chapter T2 and T3 Problems

- T2S.5: (a) What is the downward gravitational force on the balloon?
Don't forget the gas inside the balloon! (b) The density is
mass/volume. The right hand sie of (T2.26) involves the
ratio M_A/R = (1/k_B)(M_A/N_A). How is this ratio related
to the total mass and number of molecules in the gas? Use
this and the ideal gas law to rewrite the right hand side
of (T2.26) and show that this gives the density. (c) What
is your estimate of the total payload? What is the inside
and outside gas mostly made of? How do the different inside and
outside temperatures enter?
- T2R.2: (a) Follow the hints. (b) Remember exponential decay of
radioactivity? (c) What fraction of the air must leave before
you black out? Give an order of magnitude. (d) What is the
average kinetic energy of molecules in a gas at temperature
T?
- T3B.6: What is the meaning of "compressing isothermally"? What does
the ideal gas law state?
- T3S.4: Characterize each leg of the 3-cycle as isobaric, isochoric,
isothermal, etc. (whatever applies). Then figure out the heat,
work and chane in thermal energy for each leg. See Section 3.5
how to compute the net work (watch out for the direction of
the work cycle!)
- T2A.1: (a) Write down all of the forces acting on the
cylindrical parcel and balance them. The difference between
the pressure forces is dP*A. PV = NkT means the number
density of air is N/V = P/kT; what is the mass density
of air?
(b) Look for an exponential solution to Equation (T2.28).

Your comments and
suggestions are appreciated.

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**Physics H133: Hints for Problem Set 14.**

Last modified: 06:25 am, April 29, 2012.

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