Page 32 - Bruno Linder Elementary Physical Chemistry

August 25, 2010 9:36 9in x 6in b985-ch02 Elementary Physical Chemistry

The First Law of Thermodynamics 17

2.9. Relation of ∆U to q V (q at constant volume)

Consider an expansion against a constant external pressure P ext .There is
only PV work.

∆U = q − P ext ∆V (2.10)
dU =dq − P ext dV (2.11)

If the volume is constant,

∆U = q V (2.12)

dU =dq V (2.13)
These are useful relations, because they allow the internal energy change to
be obtained from measurements of q V , say in a bomb calorimeter. However,
chemists as a rule do not work with constant volumes. Question: Is there
a state function which can be simply related to q P , the heat at constant
pressure? There is! That function is the enthalpy, H, defined as

H = U + PV (2.14)

(H is a state function, because U is and so are P and V .)
Consider a change at constant pressure P. Then,

∆H =∆U + P∆V (2.15)

If there is only PV work, then at constant pressure, with P ext = P,
∆U = q P + w PV = q P − P∆V (2.16)

and

∆H = q P (2.17a)

dH =dq P (2.17b)
It is important to keep in mind that the above relation is valid only if there
is no work other than PV work. If there is other work, w other , the change
in H at constant temperature will be

∆H = q P + w other (2.18)