Using the first law of thermodynamics ( d U = d W + d Q ) we can determine the work done through an adiabatic ( d Q = 0 ) expansion by using the chain rule ( d U = ε ε a T 4 d V + 4 ε ε a V T 3 d T ) and setting it equal to d W V = − − P d V = − − 1 3 ε ε a T 4 d V .