END; include ("common_short.php"); physics_header("",""); print <<Physics H133: Problem Set #\$ps_num 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.

1. 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.?
2. 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?
3. 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?
4. 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).