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Ice Ice Liquid Water and Water vapor
and water water vapor
Warming
water
Phase
Phase change
change
Temperature (°C) 100 Boiling

Melting Warming
0
Warming

A B
–20
FIGURE 4.19 (A) Work is done against gravity to lift an object,
Constant heat input (cal)
giving the object more gravitational potential energy. (B) Work is
FIGURE 4.18 This graph shows three warming sequences done against intermolecular forces in separating a molecule from a
and two phase changes with a constant input of heat. The ice solid, giving the molecule more potential energy.
warms to the melting point, then absorbs heat during the phase
change as the temperature remains constant. When all the ice
that every gram of ice that melts in your cooler absorbs 80.0 cal
has melted, the now-liquid water warms to the boiling point,
where the temperature again remains constant as heat is absorbed of heat. Every gram of water that freezes releases 80.0 cal. Th e
during this second phase change from liquid to gas. After all the total heat involved in a solid- liquid phase change depends on
liquid has changed to gas, continued warming increases the tem- the mass of the substance involved, so
perature of the water vapor.
Q = mL f
heat of ice. When the temperature reaches the melting point equation 4.5
(0°C), it stops increasing as the ice begins to melt. More and
where L f is the latent heat of fusion for the substance involved.
more liquid water appears as the ice melts, but the temperature

Refer again to Figure 4.18. After the solid-liquid phase
remains at 0°C even though heat is still being added at a con-
change is complete, the constant supply of heat increases the
stant rate. It takes a certain amount of heat to melt all of the
temperature of the water according to Q = mcΔT, where c is
ice. Finally, when all the ice is completely melted, the tem-
now the specific heat of liquid water. When the water reaches

perature again increases at a constant rate between the melting
the boiling point, the temperature again remains constant

and boiling points. Then, at constant temperature the addition
even though heat is still being supplied at a constant rate. Th e
of heat produces another phase change, from liquid to gas.
quantity of heat involved in the liquid-gas phase change again

The quantity of heat involved in this phase change is used in
goes into doing the work of overcoming the attractive molecu-
doing the work of breaking the molecule-to-molecule bonds
lar forces. This time the molecules escape from the liquid state

in the solid, making a liquid with molecules that are now free
to become single, independent molecules of gas. Th e quantity
to move about and roll over one another. Since the quantity
of heat (Q) absorbed or released during this phase change is
of heat (Q) is absorbed without a temperature change, it is
called the latent heat of vaporization (L v ). The latent heat of

called the latent heat of fusion (L f ). The latent heat of fusion

vaporization is the heat involved in a liquid-gas phase change
is the heat involved in a solid-liquid phase change in melting or

where there is evaporation or condensation. The latent heat
freezing. You learned in chapter 3 that when you do work on
of vaporization is the energy gained by the gas molecules as
something, you give it energy. In this case, the work done in
work is done in overcoming molecular forces. Thus, the escap-

breaking the molecular bonds in the solid gave the molecules
ing molecules absorb energy from the surroundings, and a

more potential energy (Figure 4.19). This energy is “hidden,”
condensing gas (or vapor) releases this exact same amount of
or latent, since heat was absorbed but a temperature increase
energy. For water, the latent heat of vaporization is 540.0 cal/g

did not take place. This same potential energy is given up when
(970.0 Btu/lb). This means that every gram of water vapor that

the molecules of the liquid return to the solid state. A melt-
condenses on your bathroom mirror releases 540.0 cal, which
ing solid absorbs energy, and a freezing liquid releases this

warms the bathroom. The total heating depends on how much
same amount of energy, warming the surroundings. Th us, you
water vapor condensed, so
put ice in a cooler because the melting ice absorbs the latent
heat of fusion from the beverage cans, cooling them. Citrus Q = mL v
orchards are flooded with water when freezing temperatures

equation 4.6
are expected because freezing water releases the latent heat of
fusion, which warms the air around the trees. For water, the where L v is the latent heat of vaporization for the substance

latent heat of fusion is 80.0 cal/g (144.0 Btu/lb). Th is means involved. The relationships between the quantity of heat
100 CHAPTER 4 Heat and Temperature 4-16