In this problem you are to consider an adiabatic expansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.
Assume that the gas is initially at pressure , volume , and temperature . In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is .
Note that, unless explicitly stated, the variable should not appear in your answers. If needed, use the fact that for an ideal diatomic gas.
A) Find an analytic expression for , the pressure as a function of volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the given initial values , , and .
B) At the end of the adiabatic expansion, the gas fills a new volume , where . Find , the work done by the gas on the container during the expansion.
Express the work in terms of , , and . Your answer should not depend on temperature.
C) Find , the change of internal energy of the gas during the adiabatic expansion from volume to volume .
Express the change of internal energy in terms of , , and/or .
