Meteo 431  Atmospheric Thermodynamics  Spring 2002

Problem set # 6

assigned:    16 February 2002

due:            22 February 2002

1. Free expansion. Suppose that we took 103 Walker, made it air-tight and thermally insulated. We put a partition down the middle and pump all the air out of ½ of the room. Assume a pressure of 980 hPa and a temperature of 295 K.

a. If we rupture the partition so that the molecules can fill the room, what is the total entropy change?

b. How much work was required to pump out ½ of the room?

c. How many hours could you run a computer that consumes 200 watts with this amount of energy?

d. What is the enthalpy change of the air in 103 Walker Building if we change the temperature from 280 K to 300 K?

2. Consider two volumes of dry air, isolated from the environment and originally at different temperatures. They mix completely adiabatically at constant pressure, and the temperature becomes uniform. Assume the larger volume has mass of 10000 kg and a temperature of 290 K. The smaller volume has a mass of 5000 kg. The pressure of both volumes is 1000 hPa.

a. What is the final temperature if the initial temperature of the small volume is 320 K?

b. What is the final volume?

c. Calculate and plot the change in entropy as a function of the initial temperature of the small volume, from 270 K to 330 K. (I showed a calculation for the non-mixing, constant volume case in class. In this case, you must consider the effects of both temperature and volume changes, as in equations 4.56 and 4.57.)