TEMPERATURE AND HEAT
As close to chemistry as we can get
Temperature




Temperature and heat are
often used interchangeably
Temperature is a measure of
how “hot” or “cold” an object
is
Thermometers are objects that
measure temperature.
Thermometers work by putting
them in contact with the object
whose temperature we want
to measure and waiting until
reading is steady

Thermometer has reached
Thermal Equilibrium
Zeroth Law of Thermodynamics



If A is in thermal
equilibrium with C and B
is in thermal equilibrium
with C, then A and B are
in thermal equilibrium
Two objects are in
thermal equilibrium if
and only if they have
the same temperature.
A thermometer actually
measures its own
temperature.
Temperature Scales

Celsius


Water Freezes at 0, Boils
at 100
Fahrenheit
Tf 

Kelvin



9
5
T C  32
Gas thermometers use the
pressure of the gas to
determine temperature.
At -273.15oC the pressure
of the gas would reach
zero
DON’T EVER USE
“degrees” Kelvin
Linear Expansion


Materials expand when
heated (exceptions include
water)
If the difference in
temperature is not too big,
the change in length is
directly proportional to
the change in temperature
 L   L0  T

Where α is the coefficient
of thermal expansion (K-1)
Linear and Bulk Expansion


β is the coefficient of volume expansion (K-1)
For solids β=3α
Serway 19-18

At 20.0oC an aluminum ring has an inner diameter
of 5.000 cm and a brass rod has a diameter of
5.050 cm. (a) If the ring is heated, what
temperature must it reach so that it will just slip over
the rod? (b) What if? If both were heated together,
what temperature must they both reach so that the
ring slips over the road? Would the latter process
work?

Holes expand with the material
 L   L0  T
L  L 0 (1    T )
a ) 5 . 050  5 . 000 [1  24 . 0 x10
6
C
1
(T  20 . 0  C )]
T  437  C
b ) 5 . 050 [1  24 . 0 x10
6
C
1
(T  20 . 0  C )]  5 . 000 [1  19 . 0 x10
T  3000  C

Aluminum melts at 660oC
6
C
1
(T  20 . 0  C )]
Heat







When you put a warm object in
thermal contact with a cold
object, energy will transfer from
the hot object to the cold one.
This energy transfer is called
heat flow, or heat.
unit of heat calorie (cal)
Symbol is Q
Defined as the amount of heat
required to raise the temperature
of 1 gram of water from 14.5oC
to 15.5oC.
1cal =4.186J (SI unit still J)
A food value calorie is actually 1
kcal
Specific Heat

Specific Heat, c, of a
material to is the quantity
of heat needed to raise
the temperature of a
material of mass m from
T1 to T2. It is proportional
to ∆T.




Molar Heat capacity
Sometimes its easier to use
number of moles rather
than mass.
n is the number of moles
M is the mass per mole
Q  mc  T
c

m  nM
1 dQ
Q  nMc  T
m dT
Q  nC  T
Specific heat capacity of
water is 4190 J/kgK
C 
1 dQ
n dT
 Mc
Phase changes



Phase – specific state of
matter (solid, liquid, gas)
Phase change or phase
transition – when matter
changes from one phase
to another
Phase change occurs at
a specific temperature
and pressure

Ex. Water freezes at
0oC and 1 atm
Latent Heat of Fusion


Given 1kg of Ice at 1 atm, if
we begin heating it slowly, the
temperature of the ice will not
increase above 0oC until all
the ice has melted – it has
achieved phase equilibrium
Latent Heat of Fusion – Lf, is
the amount of heat needed
per unit mass to convert
matter from solid to liquid (ex.
Lf of ice is 3.34x105 J/kg)
Q melt  mL

f
same amount of heat is
needed to freeze object
Q freeze   mL
f
Latent Heat of Vaporization

Same as before
except for liquid to
gas (Lv of water is
2.256x106 J/kg)
Q   mL v
Supercooling

Supercooling – very
pure liquid can be
cooled below its
freezing point,
resulting in an unstable
state. Any slight
agitation or crystal
can cause the liquid to
turn to solidify
Superheating

Superheating – very pure liquid can be heated
above its boiling point, resulting in an unstable
state. Any slight agitation will cause bubbles to
form. It usually causes boiling liquid to be flung
everywhere so be careful when heating water in a
microwave
Example

What mass of steam, initially 130oC, is needed to
warm 200g of water in a 100g glass container
from 20.0oC to 50.0oC
Example

Heat lost by steam will be heat gained by the water
Q cold   Q hot

Steam will cool, become water, and cool once more
 130-100
Q  mc  T
Q  m s ( 2010 )( 100  130 )
Q   m s ( 6 . 03 x10 )
4
 Steam
becomes water
Q   m s ( 2 . 26 x10 )
6
 Water 100-50
Q  m s ( 4190 )( 50  100 )
Q   m s ( 2 . 09 x10 )
5
Example

Total Q
Q Total   m s ( 2 . 53 x10 )
6
Q cold   Q hot
Q cold  Q water  Q glass
Q cold  0 . 2 ( 4190 )( 50  20 )  0 . 1( 837 )( 50  20 )
Q cold  2 . 77 x10 J
4
2 . 77 x10 J  m s ( 2 . 53 x10 )
4
m s  10 . 9 g
6
Mechanisms for Heat Transfer


Conduction – occurs
between objects in
contact. Hotter atoms
will have more kinetic
energy and will jostle
neighbouring atoms,
giving some of their
energy. Atoms don’t
move.
Metals are good
conductors because free
electrons transfer
energy as well
Conduction


Heat will flow from
higher to lower
temperatures.
Heat current, H - amount
of heat transferred per
unit time (J/s)
H 
dQ
dt
 kA
T H  TC
L
A is cross sectional area
of contact, L is the
lenght.
T  T C is the
 H
L
temperature
gradient

Conduction



Constant k depends on
the material.
Higher k, better
conductor
Thermal resistance, Ropposite to conduction
H 
dQ
 A
T H  TC
dt
R
R 
L
k
Example

Two slabs of thickness L1 and L2 and thermal
conductivity k1 and k2 are in contact with each
other as shown. Determine the temperature at the
interface and the rate of energy transfer by
conduction. Assume steady state conduction
Example

Steady State conduction just means that energy
flows at one rate all through out.
H 1  k1 A
H 2  k2 A
T  TC
L1
TH  T
k1 A
T  TC
L2
T 
H 
L1
 k2 A
TH  T
L2
K 1 L 2 T c  K 2 L1T H
K 1 L 2  K 2 L1
A (TH  TC )
L1
k1

L2
k2
Convection


Transfer of heat by mass motion of a fluid (ex. Air)
Hot air rises and cool air sinks. The process is
complicated (due to turbulence) and no easy
equations exist.
 Heat
current due to convection proportional to surface
area
 Viscosity of a fluid slows down convection
 Heat current is proportional to 5/4 power the
temperature difference between the surface and the
main body of the fluid.
Radiation



Transfer of heat through electromagnetic waves
Best example, heat from the sun.
Everything emits energy in the form of EM radiation
H  Ae  T

4
Where
e
– emissivity, ratio of rate of radiation from a surface
to an ideal surface
 σ-Stefan-Boltzmann Constant = 5.670400(40)x10-8
W/m2K4
Radiation and Absorption

While an object is radiating, it will also absorb
heat.
H net  Ae  (T  T s )
4


4
If e is 1, that means it is an ideal absorber/radiator
of energy. Called a black body
If e=0, it is an ideal reflector
Serway 20.47

The sun has a surface temperature of about 5800K.
The radius of the sun is 6.96x108m. Find energy
radiated by the sun per second. e=0.965
Young and Freedman 17.25

A glass flask with a volume of 1000.00cm3 a at
0.0oC is completely filled with mercury. When the
flask and the mercury are heated to 55.0oC,
8.95cm3 of mercury overflows. If coefficient of
volumetric expansion of mercury is 18.0x10-5K-1,
What is the volume expansion of the flask?
Giancoli 14-18

A 1.20 kg hammer head is travelling at 6.5 m/s
before it strikes a 14.0 g nail and is brought to a
rest. Assuming the nail absorbs all the energy, what
is its temperature after 10 such hammer blows.
Young and Freedman 17.60

A glass vial containing a 16.0 g sample of an
enzyme cooled in an ice bath. The bath contains
water and 0.120kg of ice. The sample has specific
heat of 2250J/kgK; the vial has mass 6.00g and
specific heat 2800J/kgK. How much ice melts in
cooling the enzyme from room temperature
(19.5oC) to the temperature of the ice bath.
Young and Freedman 17.70


A long rod, insulated from the sides is in perfect contact
with boiling water and an ice water mixture. The rod
consists of 1.00m section of copper and a length L2 of
steel. Both sections have a cross sectional area of
4.00cm2. The temperature of the copper/steel junction
is 65.0oC after steady-state has been setup. (a) How
much heat per second flows from boiling water to the
ice-water mixture?(b) What is the length of L2?