Question

the first question is done I need the others

Consider a closed system that cannot do pressure volume work, but rather does work of the form w = (xar The state variables for this system are n, T, X, and Y, and where X > 0. For this system dU = TAS + XDY la (7 pts) Using the definition of A derive an expression for dA for this system and derive th corresponding Maxwell relation. an (4 pts) Derive an expression for Guy in terms of X and T. (3 pts) If the equation of state for this system is X = T/Y”, where a is a constant, prov that ut = 0. (6 pts) If U = U(T,Y), derive an expression that shows how a change in Y (DY) is relate to a change in T (dT) for an adiabatic process. You will need to use both the first la of thermodynamics and the total differential of U in your derivation. If Y increases in a adiabatic process, what happens to T?

Answer 1

Answer (b)

dU= TdS + XdY

Differentiating the above equation with respect to dY at constant temperature we get,

(dU/dY)
_T = T *
AP/SP)
^_T + X

Answer (d)

U= U(T,Y)

Applying first principle of differentials,

dU= (
SUST
)_Y * dT + (
SU/SY
)_T * dY

For an adiabatic process, dU=0 hence the above equation becomes

(
SUST
)_Y * dT = -  (
SU/SY
)_T * dY

since according to above equation Y and T are oppositely charged, when Y increases T decreases and vice-versa.