When a certain polyatomic has undergoes adiabatic expansion, it’s pressure p and volume V satisfy the equation pV^1.3 = k, where k is a constant. Find the relationship between the rates of change in pressure and volume over time. Show and explain each step please.

Answer 1

using the product rule,
dp/dt * v^1.3 + p*1.3 v^0.3 dv/dt = 0
so, I guess you could say that
(dp/dt)/(dv/dt) = -1.3p/v

or, by rearranging the 1st equation,
p = kv^-1.3
dp/dt = -1.3kv^-2.3 dv/dt
(dp/dt)/(dv/dt) = -1.3k/v^2.3