The fundamental equation of a certain material is 1 2 u m n n s v   ( ) / where m is a positive constant. it is desired to do some processing of this material in which t, v, n1 and 2 are controlled. what legendre transform will transform the fundamental equation into the one of the form x = x ( t, v, n1 , 2 ) a) derive the equivalent gibbs equation for this transform. b) derive the equivalent euler equation (integrated gibbs equation) for this transform. c) show that 1 2 2 1 1 , , t v, , n v s n t                     d) find the new fundamental equation in the transformed representation, i. e., find the function x = x( t, v, n1 , 2 )