Certain stars are fully convective. in this case, we can approximate the relationship between pressure and density as: (1) dlog(p) dlog() the adiabatic index 7 is in general a function of thermodynamic variables, e. g. p and p, but can be approximated as constant and equal to 5/3 for a gas with a fixed ionisation fraction. 1. for a constant 7, show that p() obeys a power-law for some constant k: 2 p=kp? 2. for a fully-convective star where dt/dr is determined by this adiabatic index y and not radiation, find alternative equations for stellar structure based on the three derivatives dm dr', d log(p)/dr and d log(t)/dr', where m' = m/m. and r = r/r.. show all working. hint - first convert the dp/dr' equation to d log(p)/dr']