Physics 1B - Tutorial #3

1. All the processes shown below have the same inital pressure (2 atm = 2 x 10⁵Pa) and volume (100 cm³) and end at the same values of pressure (2 atm) and volume (300 cm³). Which diagrams represent the same amount of work done by the system?

   W = PdV = Area under the PV curve.

   • a) In this case we have expansion at constant pressure; the system is doing work on its surroundings. W = P V (because P=const) = (2 x 10⁵Pa) x (200 x 10^-6m³) = 40 J.
   • b) & c) have the same area, so the work is the same.
   • d) the area under the curve is somewhat less than that of a), b) & c).
   • e) the box at the end represents negative work (note ccw path) hence the work is less than that of a), b) or c).

2. Starting from the point shown sketch

3. For each case below describe whether the diagram represents a possible (i.e. does not violate the Laws of Thermodynamics) heat engine or refrigerator. If not describe what is wrong.
   • a) This has heat transferred from high T to low T, doing work in the process like a heat engine, except that the energy out is greater than the energy in so it violates the First Law. IMPOSSIBLE!
   • b) This is a heat engine that conserves energy. Maximum Efficiency = (T_H - T_C)/T_H = (600K - 300K)/600K = 50% You can get up to 5J of workl out so this is OK.
   • c) This violates the Second Law of Thermodynamics in a big way. You cannot move heat from colt to hot region without putting work in. IMPOSSIBLE.
   • d) This is a refrigerator, using work to move heat from cold region to a warm region.

4. On a warm day your roommate suggests that you leave the refrigerator door open to "cool this place down." After a while with the fridge door open will the room be cooler, the same or warmer? Explain.

   The initial blast of cold air may feel good, but close the door fast! This will heat up the room further. The energy that you must use to operate the refrigerator is transformed into heat and exhausted into the room, so more heat is introduced into the room than is removed. Note that an air conditioner exhausts the heat to the outdoors. OK

Physics 1B Home   Tutorials   Tutorial #2   Tutorial #4