Question
I dont know where to start...
Components of U The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function meaning that any path used in calculating delta T will result in the same answer. For any pure substance or fixed mixture of substances, the internal energy. U. can be determined from any two of the variables P, V, and T. It is often most convenient to choose V and T as the variables. It is helpful, then, to examine how U depends on V and T independently. Because U is a state function, delta U only depends on Vi, Ti and Vf, Tf. The cyclic rule can be used to rewrite the differential in terms of the information available. Recall the cyclic rule uses each variable in the numerator once, the denominator once, and as the fixed value once. So for variables x, y, and z, it would be written The Dependence of U on V Given the relationship use the cyclic rule to write, , in terms of the measurable quantities P, beta, T, and K. Recall that beta and K are the isobaric volumetric thermal expansion coefficient and the isothermal compressibility, respectively, defined by Express your answer in terms of P, beta, T, and K.
Explanation / Answer
by cyclic rule (dz/dy)X = -1 /( dZ/dx)Y (dx/dy)z)
( dU/dV)t = T( dP/dT)v -P
now let us consider (dP/dT)v part
by cyclic rule (dP/dT)v (dT/dV)p (dV/dP)t = -1
(dP/dT)v = -1 ( dV/dT)p ( dP/dV) T
= - BV /-kV = B/K ( B= beta)
hence (dU/dV)t = T( B/K) -P
