In 9A we learned that if work is done on an object by a conservative force as it
ID: 1794955 • Letter: I
Question
In 9A we learned that if work is done on an object by a conservative force as it moves from point A to point B, then we can invent a function related to this force called a “potential energy function” that is defined at every point in space. The advantage of this function is that the change in the object’s energy due to this force can be computed by simply finding the change in this potential energy (rather than performing a complicated line integral). In thermodynamics, we can do a similar trick. Like work, heat exchange depends intimately upon the process involved, but if we know the type of process, we can define a function called a thermodynamic potential , which is a state function whose change in value equals the heat exchanged. [Until part (c), you should not make any assumptions about the system, i.e. it is not necessarily an ideal gas.]
a. Show that for an isochoric process, the internal energy is the thermodynamic potential.
b. Another thermodynamic potential is called “enthalpy,” and which the state function defined by: H (U , P , V ) = U + PV . Show that this is the thermodynamic potential that applies to isobaric processes. [Hint: the change in H from state A to state B is the integral of dH. Write dH in terms of small changes of U, P, and V, and go from there. ]
c. Show explicitly for an ideal gas that the change in enthalpy between two states equals the heat exchanged, when the process is isothermal.
Explanation / Answer
a
isochoric process-process in which volume remain constant
Q = du +W
In isochoric process W = pdv = 0
Q = du , now since Q depends on the state , du is a state function.
b) H= U+PV
dH = du + Pdv + V dP
in isobaric process dP =0
dH = du + PdV = dU +W = Q
c)
H = U+PV
dH = dU+ pdV +v dP
pv = nRT
pdV +VdP = nRdT = for isothermal process - So dH = dU