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  • Examine heat transfer.
  • Calculate final temperature from heat transfer.

So far we have discussed temperature change due to heat transfer. No temperature change occurs from heat transfer if ice melts and becomes liquid water (i.e., during a phase change). For example, consider water dripping from icicles melting on a roof warmed by the Sun. Conversely, water freezes in an ice tray cooled by lower-temperature surroundings.

The given figure shows a vertically downward, knife-shaped ice piece, with water droplets sparkling on its surface.
Heat from the air transfers to the ice causing it to melt. (credit: Mike Brand)

Energy is required to melt a solid because the cohesive bonds between the molecules in the solid must be broken apart such that, in the liquid, the molecules can move around at comparable kinetic energies; thus, there is no rise in temperature. Similarly, energy is needed to vaporize a liquid, because molecules in a liquid interact with each other via attractive forces. There is no temperature change until a phase change is complete. The temperature of a cup of soda initially at C stays at C until all the ice has melted. Conversely, energy is released during freezing and condensation, usually in the form of thermal energy. Work is done by cohesive forces when molecules are brought together. The corresponding energy must be given off (dissipated) to allow them to stay together [link] .

The energy involved in a phase change depends on two major factors: the number and strength of bonds or force pairs. The number of bonds is proportional to the number of molecules and thus to the mass of the sample. The strength of forces depends on the type of molecules. The heat Q size 12{Q} {} required to change the phase of a sample of mass m size 12{m} {} is given by

Q = mL f  (melting/freezing), size 12{Q= ital "mL" rSub { size 8{f} } } {}
Q = mL v  (vaporization/condensation), size 12{Q= ital "mL" rSub { size 8{v} } } {}

where the latent heat of fusion, L f size 12{L rSub { size 8{f} } } {} , and latent heat of vaporization, L v size 12{L rSub { size 8{v} } } {} , are material constants that are determined experimentally. See ( [link] ).

Figure a shows a four by four square lattice object labeled solid. The lattice is made of four rows of red spheres, with each row containing four spheres. The spheres are attached together horizontally and vertically by springs, defining vacant square spaces between the springs. A short arrow points radially outward from each sphere. The arrows on the different spheres point in different directions but are the same length, and one of them terminates at a dashed circle that is labeled limits of motion. To the right of this object are shown two curved arrows. The upper curved arrow points rightward and is labeled “energy input” and “melt.” The lower arrow points leftward and is labeled “energy output” and “freeze.” To the right of the curved arrows is a drawing labeled liquid. This drawing contains nine red spheres arranged randomly, with a curved arrow emanating from each sphere. The arrows are of different lengths and point in different directions.Figure b shows a drawing labeled liquid that is essentially the same as that of figure a. To the right of this drawing are shown two curved arrows. The upper curved arrow points rightward and is labeled “energy input” and “boil.” The lower arrow points leftward and is labeled “energy output” and “condense.” To the right of the curved arrows is another drawing of randomly arranged red spheres that is labeled gas. This drawing contains eight red spheres and each sphere has a straight or a curved arrow emanating from it. Compared to the drawing to the left that is labeled liquid, these arrows are longer and the red spheres are more widely spaced.
(a) Energy is required to partially overcome the attractive forces between molecules in a solid to form a liquid. That same energy must be removed for freezing to take place. (b) Molecules are separated by large distances when going from liquid to vapor, requiring significant energy to overcome molecular attraction. The same energy must be removed for condensation to take place. There is no temperature change until a phase change is complete.

Latent heat is measured in units of J/kg. Both L f size 12{L rSub { size 8{f} } } {} and L v size 12{L rSub { size 8{v} } } {} depend on the substance, particularly on the strength of its molecular forces as noted earlier. L f size 12{L rSub { size 8{f} } } {} and L v size 12{L rSub { size 8{v} } } {} are collectively called latent heat coefficients . They are latent , or hidden, because in phase changes, energy enters or leaves a system without causing a temperature change in the system; so, in effect, the energy is hidden. [link] lists representative values of L f size 12{L rSub { size 8{f} } } {} and L v size 12{L rSub { size 8{v} } } {} , together with melting and boiling points.

The table shows that significant amounts of energy are involved in phase changes. Let us look, for example, at how much energy is needed to melt a kilogram of ice at C to produce a kilogram of water at 0 ° C . Using the equation for a change in temperature and the value for water from [link] , we find that Q = mL f = ( 1 . 0 kg ) ( 334 kJ/kg ) = 334 kJ is the energy to melt a kilogram of ice. This is a lot of energy as it represents the same amount of energy needed to raise the temperature of 1 kg of liquid water from C to 79 . C . Even more energy is required to vaporize water; it would take 2256 kJ to change 1 kg of liquid water at the normal boiling point ( 100º C size 12{"100"°C} {} at atmospheric pressure) to steam (water vapor). This example shows that the energy for a phase change is enormous compared to energy associated with temperature changes without a phase change.

Questions & Answers

What interference
Moyinoluwa Reply
What is a polarized light called?
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
what is radioactive element
Half of the total time required by a radioactive nuclear atom to totally disintegrate
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
state the laws of refraction
state laws of reflection
Why does a bicycle rider bends towards the corner when is turning?
When do we say that the stone thrown vertically up wards accelerate negatively?
Give two importance of insulator placed between plates of a capacitor.
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
when was the name taken from
Biola Reply
retardation of a car
when was the name retardation taken
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
is not just a material
it is the surface of a metal
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
pls what is mirage
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
what is the dimensional formula for torque
Otto Reply
same units of energy
what is same units of energy?
M L2 T -2
it is like checking the dimension of force. which is ML2T-2
M L2 T-2
what is the significance of moment of inertia?
an object of mass 200g moves along a circular path of radius 0.5cm with a speed of 2m/s. calculate the angular velocity ii period iii frequency of the object
Faith Reply
w = 2/(0.005) period = PIE(0.005) f = 1/(PIE(0.005)) assuming uniform motion idk..
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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