Assignment:
Problems:
1 (a) The temperature near the top of Saturn's cloud layer is about 110K. The temperature at the top of the earth's troposphere, at an altitude of about 20km, is about 220K. Calculate the rms speed of hydrogen (H2) molecules in both these environments. Give your answers in m/s and as a fraction of the escape speed from the respective planet.
(b) Hydrogen gas is a rare element in the earth's atmosphere. In the atmosphere of Saturn, by contrast, 96% of all molecules are H2. Explain why.
(c) Suppose an astronomer claims to have discovered an oxygen (O2) atmosphere on the Moon. How likely is this to be true? The Moon has a surface temperature of about 220K near its equator.
2. 20.0L of an ideal diatomic gas at 1.00 atm and 300 K are contained in a cylinder with a piston. The gas first expands isobarically to twice its original volume (step 1). It is then compressed isothermally back to its original volume (step 2), compressed isobarically to half its original volume (step 3), and finally allowed to expand isothermally back to its original volume (step 4).
a) Show the series of processes on a pV diagram.
b) Calculate the temperature, pressure, and volume of the system at the end of each step in the process. Indicate the values of the isothermal processes on the pV diagram.
c) Compute the total work done by the gas on the piston during each step of the cycle, both in Joules and in L-atm, and the total work done by the gas for one complete cycle.
d) Compute the heat added during each step of the cycle, both in Joules and in L-atm, and the total heat added for one cycle. Compare the total work done with the total heat added.
3. 20.0L of an ideal monatomic gas at 1.00 atm and 300 K are contained in a cylinder with a piston. The gas first heats up isochorically to twice its original pressure (step 1). It then expands isothermally to twice its original volume (step 2), cools down isochorically back to its original temperature (step 3), and finally compresses isothermally back to its original pressure (step 4).
a) Show the series of processes on a pV diagram.
b) Calculate the temperature, pressure, and volume of the system at the end of each step in the process. Indicate the values of the isothermal processes on the pV diagram.
c) Compute the total work done by the gas on the piston during each step of the cycle, both in Joules and in L-atm, and the total work done by the gas for one complete cycle.
d) Compute the heat added during each step of the cycle, both in Joules and in L-atm, and the total heat added for one cycle. Compare the total work done with the total heat added.
4. A 0.25L container is initially filled with air at STP. A piston compresses it adiabatically to a volume of 12.0% of the original volume. The air may be treated as an ideal gas withγ =1.40.
(a) Calculate the final temperature and pressure.
(b) Sketch a pV-diagram for this process. On this diagram also draw the isotherms for the initial and final temperatures.