Page 34 - Basic physical chemistry for the atmospheric sciences

20 Basic physical chemistry

mass of the system is p(a2 - a 1). Therefore, from Eq. (2. 6 ) , the heat d q
added to a unit mass of the system at constant pressure is given by
d = (u 2 - u1) + p(a2 - a1 ) = (u2 + pa2) - (u1 + pa1)
q
where u1 and u2 are, respectively, the initial and final i n ternal energies
for unit mass. Therefore, at constant pressure,
(2.7)

where h is the enthalpy (sometimes called the heat at constant pres­
sure) of a unit mass of the system, which is defined by
_
h = u + p a (2. 8 )

If the quantity of heat (in joules) required to raise a unit mass of the
1
system by ° C at constant pressure (called the specific heat at constant
pressure) is cP, then

dq = c dT (2.9)
P
s
From Eq . (2. 7) and (2.9)
dh = c dT (2. 1 0 )
p
or, on integrating,
(2. 1 1 )

where the value of h is taken to be zero at the absolute zero of
temperature T = OK).
(
Exercise 2 . 1 . A parcel of dry air at l atm pressure receives 1 0 7 J of
heat by radiation from the sun, and its volume increases by 22 m3• If
the center of the mass of the parcel does not move, what is the change
in the internal energy of the parce ? If the molecules in the air exert no
l
forces on each other, what is the increase in the temperature of the air
parcel if it has a mass of 8000 kg? (Specific heat at constant pressure
1
1
1
of dry air = 0 04 J deg-1 kg- . )
1
Solution. Since the center of mass of the parcel does not move ,
there is no change in either the macroscopic potential energy or the
kinetic energy of the parcel. Also, the pressure of the system remains
constant at I atm = . 0 1 3 bar = . 0 1 3 x 105 Pa. Therefore, the first law
1
l
of thermodynamics in the form of Eq. (2.6) applies, which, for a
system as a whole (rather than a unit mass), can be written
dQ = dU +pdV (2 . 12)