Page 139 - Physical chemistry understanding our chemical world

106 ENERGY AND THE FIRST LAW OF THERMODYNAMICS

Integrating yields

(H 2 − H 1 ) = C p (T 2 − T 1 ) (3.23)
where the term on the left-hand side is H. Equation (3.23) relates to a single, pure sub-
stance.
If we consider a chemical reaction in which several chemicals combine, we can write
an expression like this for each chemical. Each chemical has a unique value of H and
C p , but the temperature change (T 2 − T 1 ) remains the same for each.
We combine each of the H terms to yield H O (i.e. H O at T 2 )and H O .
r T 2 r r T 1
Combining the C p terms according to Equation (3.22) yields C p . Accordingly, Equa-
tion (3.23) then becomes Equation (3.21), i.e.:
O O
H = H + C p (T 2 − T 1 )
r T 2 r T 1

Why does water take longer to heat in a pressure
cooker than in an open pan?

The differences between C V and C p

A pressure cooker is a sealed cooking pan. Being sealed, as soon as boiling occurs,
the pressure of steam within the pan increases dramatically, reaching a maximum
pressure of about 6 × p , causing the final boiling temperature to
O
Seep. 199to seewhy increase (see Fig. 5.12 on p. 200). Unlike other pans, the internal
a pressure cooker can volume is fixed and the pressure can vary; the pressure in most
cook faster than a con- pans is atmospheric pressure (∼ p ), but the volume of the steam
O
ventional, open pan. increases continually.
The heat capacity of the contents in a pressure cooker is C V
because the internal volume is constant. By contrast, the heat capacity of the food
or whatever inside a conventional pan is C p . The water is a pressure cooker warms
slower because the value of C p is always smaller than C V . And being smaller, the
temperature increases faster per unit input of energy.
In fact, the relationship between C V and C p is given by
It is relatively rare
that we need C V val- C V − C p = nR (3.24)
ues; most reactions are
performed at constant where we have met all terms previously.
pressure, e.g. refluxing
aflaskatatmospheric Worked Example 3.10 What is the heat capacity C V of 1 mol of
pressure. water? Take the value of C p from SAQ 3.7.

Rearranging Equation (3.24) slightly yields

C V = nR + C p