Please print this sheet, sign the statement at the bottom,
and use it as cover page when you submit your homework. Remember to always include a
complete explanation of your reasoning, and to show all calculations.
- 0: Greek letters
Write the full Greek alphabet on one sheet of paper. Use one line for each letter and include the lower case and upper case forms of the letter, and the name of the letter.
- 1: Ideal gas expansion. I
An ideal gas has pressure equation of state pV = NkT and its internal
energy is given by E = (f/2) NkT, where f is a
constant that depends on the gas. If N particles of this gas are contained
in a cylinder whose volume is allowed to increase from V to 2V by
sliding a piston gradually until the volume reaches the desired value while the temperature
is kept constant, what is the change in the entropy of the gas?
- 2: Ideal gas expansion. II
An ideal gas has pressure equation of state pV = NkT and its internal
energy is given by E = (f/2) NkT, where f is
a constant that depends on the gas. If N particles of this gas are contained
in a thermally insulated cylinder whose volume is allowed to increase from V
to 2V by sliding a piston gradually until the volume reaches the desired value,
what is the change in the entropy of the gas? What is the change in temperature? This is an adiabatic transformation, for which its pressure and volume are related by \(pV^\gamma = \) constant, where \(\gamma\) is a parameter characteristic of the type of gas, related to f.
- 3: Ideal gas expansion. III
An ideal gas has pressure equation of state pV = NkT and its internal
energy is given by E = (f/2) NkT, where f is
a constant that depends on the gas. If N particles of this gas are contained
in a thermally insulated box of volume V and the gas is allowed to flow freely
through a hole until it fills a box of total volume 2V, what is the change in
the entropy of the gas? What is the change in temperature?
You are allowed, in fact encouraged, to discuss these problems and how to solve them with other students
in the class, but you are not allowed to copy or use in any way anyone else's written solution to any of
these problems. This includes solutions that may be provided to you by a student who took the course
previously, or solutions you may find online or in print. This policy will hold for all assignments
in this class.
Aside from oral discussions I may have had with other students in the class, the solutions
to this homework set I am submitting are entirely my own.
Name: __________________________________ Signed: ___________________________________ |
