Heat and phase changes'

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Lecture 34

• Heat and phase changes.

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Heat
We saw that energy is transferred due to a
temperature difference. There is no work involved
here. This transferred energy is called heat.
Units SI J (Joules) cal (calorie) 1 cal
heat required to raise the temperature
of 1 g of water from 14.5C to 15.5C
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Specific heat
How much heat is needed to change by ?T the
temperature of a mass m of material X?
cX does have some temperature dependence, but
very small (ie, negligible for 221)
Definition of calorie!
Water has a very high specific heat.
water c 1 cal//(g C) 4186 J/(kg K) iron
c 470 J/(kg K)
Its hard to increase the temperature of water.
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Example Kettle
Your electric kettle is labeled 2000 W. How long
will it take to boil 0.5 liter of water if the
water comes out of the tap at 15C?
Heat needed to warm up the water
Assuming that all the heat produced by the kettle
is used to warm up the water,
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But of course in reality it will be a little
longer. What are we neglecting?

• Heat produced by the internal resistance of the
  kettle also warms up
• air (negligible if kettle has a lid and is well
  insulated)
• kettle (at least internal wall)

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What does specific heat depend on?
Temperature average kinetic energy of particles
Degrees of freedom ( ways to move, ie, to
increase kinetic energy) Example A molecule of
helium is made of one atom. It can basically just
bounce around in 3 directions (3 degrees of
freedom) A molecule of hydrogen is made of two
atoms. It can bounce around (3 dof) and it can
also rotate ( 2 dof, total 5 degrees of freedom)
Molar mass Heavier molecules require more
additional energy to increase their average speed.
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Phases or states of matter

• Three basic states of matter
• Solid
• Liquid
• Gas

A phase change involves a critical change in the
microscopic structure of matter. Example Ice to
water Lattice disappears, molecules are free to
move around.
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Analysis Phase changes for water
1 kg of ice is placed on a pan on the stove. Plot
of temperature versus heat supplied by stove.
T
Q
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ACT Specific heats
Which water phase has the largest specific heat?

• Ice
• Liquid water
• Steam

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Latent heat
Water Lfusion 334 kJ/kg Lvaporization
2256 kJ/kg
This energy is not used to increase the kinetic
energy of the particles (does not increase the
temperature) but to change the structure of
matter.
During a phase change, two or more phases coexist
in dynamic equilibrium. Examples Vapor and
liquid water exactly at 100C Ice and liquid
water exactly at 0C Vapor/Liquid water/Ice at
the triple point (273.16 K and 610 Pa)
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In-class example Ice melting
How much heat is needed to turn 10 g of ice at
-5C into liquid water at 20C?

• 105 J
• 420 J
• 837 J
• 3330 J
• 4272 J

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Follow-up example Iced coffee
10 g of ice at -5C are added to 30 ml of hot
coffee inside a thermos that is then tightly
closed. After the system reaches equilibrium, the
temperature of the mix is 20C. What was the
initial temperature of the coffee?
Because the system is thermally isolated (closed
thermos), the hot coffee is the only source of
energy, so it must provide the necessary 4272 J
of heat.
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10 g of ice at -5C are added to 30 ml of hot
coffee inside a thermos that is then tightly
closed. After the system reaches equilibrium, the
temperature of the mix is 20C. What was the
initial temperature of the coffee?
Energy balance


-

Energy is released
Energy is absorbed
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Phase transition temperatures
Water at 1 atm Tmelting 0C Tboiling
100C
These temperatures indicate when the kinetic
energy of the molecules is enough to break the
structure.
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pT diagram
Melting curve (solid/liquid transition)
Critical point
solid
liquid
Vapor pressure curve (gas/liquid transition)
Triple point
gas
Sublimation curve (gas/solid transition)
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pT diagram (water)
For water, the pT diagram looks a little
different.
liquid
solid
gas
water
other
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pT diagram (water)
p
Critical point
solid
liquid
gas
T
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Triple point (water)
Triple point for water p 610 Pa (0.006 atm), T
273.16K
p
solid
Critical point
liquid
Liquid water does not exist for p lt 610 Pa!!
Triple point
gas
T
At 610 Pa Tmelting Tboiling
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Critical point (water)
Critical point for water 647K and 218 atm
Liquid and gas are indistinguishable beyond
critical point
At critical point, ?gas ?liquid
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Example Mixing oil
30 g of oil at 10C and 150 g of oil at 80C are
placed in a thermos. The thermos is closed and
the system is allowed to go to equilibrium. What
is the final temperature of the oil?
Closed thermos is an insulated system no energy
exchange with rest of the universe
Flow of heat
cold
hot
QH lt 0 (energy loss)
QC gt 0 (energy gain)
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30 g of oil at 10C and 150 g of oil at 80C are
placed in a thermos. The thermos is closed and
the system is allowed to go to equilibrium. What
is the final temperature of the oil?
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Molar heat capacity
Lets change the question
How much heat is needed to change by ?T the
temperature of n moles of material X?
n number of moles M mass of one mole (molar
mass)