H133: 1094 Session 7

Write your name and answers on this sheet and hand it in at the end.
After the indicated time, move on to the next activity, even if you are not finished!

1. T3 Group Warm-Up Problems [10 minutes]

1. Do T3T.1, putting your answers below. This is work vs. heat, as in class.

   a.	b.	c.
   d.	e.

2. Do Exercise T3X.2 without looking at the answer first. This is about thermodynamic work (W) versus center-of-mass work ("k-work"). The distinction is explained at the top of pg. 42. The key is that thermodynamic work is any energy flowing across the boundary of your system; it doesn't have to move the center of mass, but changes the system's thermal energy. When you've agreed on answers, check them on pg. T3X.2 and discuss any you got wrong.

   a.	b.	c.
   d.	e.	f.

3. Do T3T.2. Positive work means it flows in. Your basic definition is Equation (T3.6). Explain your answers.
   
   
   
   

2. Gas Properties PhET Simulation [15 minutes]

Start up the PhET applet "Gas Properties". By operating the pump, you add molecules of a gas to the box, which settles down to a pressure and temperature (but fluctuates noticably because of the small number of molecules). You can change the volume of the box (by moving the little figure), add or remove heat, and let molecules escape.

1. Pump enough times so that there are over 100 molecules. Assume that it is an ideal gas and make some measurements to calculate the volume of the box. Show your work.
   
   
   
   
2. Now add heat and/or molecules and recalculate the volume. Is it really (approximately) an ideal gas?
   
   
   
   
3. Slowly decrease the volume. What happens to the pressure and temperature? Explain the trends. Now reset and decrease the volume rapidly. Discuss the difference.
   
   
   
   
4. Let the top off the box for a few seconds, letting some molecules escape. What happens to the temperature? Explain in terms of the relationship between T and the average kinetic energy (as observed by the speed of the remaining molecules). So why does evaporation cause cooling?
   
   
   
   
5. Turn on gravity halfway on the scale. Is what you observe qualitatively consistent with the result of T2A.1 (from class). [The "Layer Tool" option may be helpful.]
   
   
   
   

3. T3 Two-Minute Drill [15 minutes]

Be careful about the sign of the work (see above) and about which direction the process is running. The processes are defined on pp. 45-46. Look at Example T3.1 first to see how to decide on the signs. Explain your answers briefly.

1. T3T.3
   
   
   
2. T3T.4
   
   
   
3. T3T.5
   
   
   
4. T3T.6
   
   
   
5. T3T.7
   

4. StatMech Program [10 Minutes]

Start up the StatMech program from the H133 home page. The program is described in chapter T4. We are simulating a solid using the Einsein model, which is pictured in Figure T4.1: atoms connected by springs. We think of each atom as being in three one-dimensional oscillators (one for each direction), with energies given by integers times hbar-omega (measuring with respect to absolute zero; what does this do?). To find the total energy, specify the integers for each atom. Let N be the number of atoms and U the total internal energy.

1. Do T4X.6, then look at the answer and correct if wrong.
   a.
   
   
   b.
   
   
   c.
   
   
   
2. Do T4B.5. Use equation (T4.7) then check with StatMech. [Set A to have 3 atoms and set total U=15, then look for U(A)=15 and U(B)=0.]