Simple Model

Use the differential equations of stellar structure and the ideal gas law as an equation of state. Make whatever assumptions you need in order to obtain a simple result, but justify the assumptions. Predict the dependence of luminosity $L$, effective surface temperature $T$, and radius $R$ on mass in the form

1. $L/L_{Sun}=(M/M_{Sun})^\alpha$
2. $T/T_{Sun}=(M/M_{Sun})^\beta$
3. $R/R_{Sun}=(M/M_{Sun})^\gamma$