Find an analytic expression for p(v), 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 p0, t0, and v0.

The drag force, fd, imposed by the surrounding air on a vehicle moving with velocity v is given by fd = cdaρv 2/2 where cd is a constant called the drag coefficient, a is the projected frontal area of the vehicle, and ρ is the air density. an automobile is moving at v = 80 kilometers per hour with cd = 0.28, a = 2.3 m2, and ρ = 1.2 kg/m3.