Page 124 - Physical chemistry understanding our chemical world

INTRODUCTION TO THERMODYNAMICS: INTERNAL ENERGY 91

gases increases as soon as energy is added, since U = q + w (Equation (3.5)).
For simplicity, in this argument we ignore the expansion of the atmosphere inside
the oven.
But what is the temperature inside the oven? And by how much does the temperature
increase? To understand the relationship between the temperature and the amount of
heat entering the system, we must first appreciate that all energies are quantized. The
macroscopic phenomenon of temperature rise reflects the microscopic absorption of
energy. During absorption, quanta of energy enter a substance at the lowest energy
level possible, and only enter higher quantal states when the lower energy states are
filled. We see the same principle at work when we fill a jar with marbles: the first
marbles fall to the jar bottom (the position of lowest potential energy); and we only
see marbles at the top of the jar when all the lower energy levels are filled. Continuing
the analogy, a wide jar fills more slowly than does a narrower jar, even when we add
marbles at a constant rate.
On a macroscopic level, the rate at which the quantal states are filled as a body
absorbs energy is reflected by its heat capacity C. We can tell how quickly the
quantum states are occupied because the temperature of a body is in direct proportion
to the proportion of states filled. A body having a large number of quantum states
requires a large number of energy quanta for the temperature to increase, whereas a
body having fewer quantum states fills more quickly, and becomes hot faster.

Why does water boil more quickly in a kettle
than in a pan on a stove?

Heat capacity

Most modern kettles contain a powerful element (the salesman’s word for ‘heater’),
−1
operating at a power of 1000 W or more. A heater emits 1 W if it gives out 1 J s ;
−1
so, a heater rated at 1000 W emits 1000 J s . We may see this
power expressed as 1 kW (remember that a small ‘k’ is shorthand The SI unit of power is
for kilo, meaning 1000). By contrast, an electrical ring on the stove the watt (W). A heater
will probably operate between 600 and 800 W, so it emits a smaller rated at a power of 1 W
amount of heat per second. Because the water absorbs less heat emits 1 J s −1 .
energy per unit time on a stove, its temperature rises more slowly.
The amount of energy a material or body must absorb for its
temperature to increase is termed its ‘heat capacity’ C. A fixed The heat capacity C
of a material or body
amount of water will, therefore, get warmer at a slower rate if the
relates the amount of
amount of heat energy absorbed is smaller per unit time.
energy absorbed when
Equation (3.6) expresses the heat capacity C in a mathematical raising its temperature.
form:
dU

C V = (3.6)
dT
V