In this problem you are to consider an adiabaticexpansion 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 p0, volume V0, and temperature T0. 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
γ = Cp/CV = 7/5.
A. Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.
B. At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion.
C. Find ΔU, the change of internal energy of the gas during the adiabatic expansion from volume V0 to volume V1.