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HEAT AND CALORIMETRY

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Title: HEAT AND CALORIMETRY


1
HEAT AND CALORIMETRY
2
What is Heat?
  • Modern definition energy transferred because of
    a difference in temperature(energy on the move)
  • 1 calorie raises the temperature of 1 gram of
    water by 1 Celsius degree.
  • 1 kilocalorie (kcal or Calorie) raises
    temperature of 1 kg of water by 1 degree Celsius
  • 1 British Thermal Unit (BTU) raises temperature
    of 1 pound of water by one degree Farenheit

3
Mechanical Equivalent of Heat
  • Discovered by James Joule
  • Falling weight makes
  • paddle turn
  • 4.186 x 103 J 1 kcal
  • Interpretation
  • HEAT IS ENERGY
  • TRANSFER

Courtesy W. Bauer http//lecture.lite.msu.edu/mmp
/kap11/cd295.htm
4
Joules Apparatus
Link to Joules original article
5
Imagine This
  • What other situations could be used to
    demonstrate the mechanical equivalent of heat?

6
Example
  • When digested a slice of bread yields 100 kcal.
    How high a hill would a 60 kg student need to
    climb to work off this slice of bread? (100
    kcal is energy released by burning the bread

100 kcal x 4.186 x 103 J/kcal 4.2 x 105 J
W mgh
h W/mg 4.2 x 105 / (60 kg)(9.80 m/s2) 714m
7.1 x 102 m
If the body is only 20 percent efficient in
transforming the bread, how high need they climb?
7
Bullet in Block
  • When a 10 g bullet traveling 500 m/s is stopped
    inside a 1kg wood block nearly all its KE is
    transformed to heat. How many kcal are released?

KE ½ mv2 0.5 x 0.010 kg x (500)2 1250 J
1250 J x 1 kcal/4186 J 0.30 kcal
8
Internal Energy, Temperature and Heat
  • The thermal energy or internal energy of an
    object is the sum total of all the energy in its
    molecules
  • (symbol U)
  • Temperature is measure of average KE per molecule
    (T)
  • Heat refers to transfer of energy
  • (symbol Q)

9
Internal Energy Does Not Include KE
  • KE of whole object represents all molecules
    moving in the same direction
  • U is random motion only

10
Internal Energy of an Ideal Gas
  • U N (1/2 mv2)
  • But 1/2 mv2 3/2kT
  • U 3/2NkT
  • U 3/2 nRT

N is total number of molecules in sample
k R/NA
U 3/2 nRT
Internal Energy of an ideal gas depends only on
temperature and number of moles
11
Specific Heat
  • How much does temperature rise when heat is put
    into something?
  • Depends on the material, the mass and the
    quantity of heat
  • Q m c DT c is specific heat in J/kg Co
  • or
  • Q n c DT c is specific heat in J/mol
    Co
  • Specific Heat of water 4.186 x 103J/kg Co

DT Q/mc
Table of Specific Heats
12
Understanding Specific Heat
  • For a given amount of heat added, temperature
    increases more for a smaller specific heat
  • Water has a very large specific heat and is
    therefore relatively difficult to heat or cool.

13
Examples
  • How much heat is required to heat 1 liter of
    water from 20 oC to 100 oC?
  • Q mcDT 1Kg x 4186 J/kg oC x 80 oC
  • 3.35 x 105 J 80 kcal
  • How much heat is required to heat 1.0 kg iron
    from 20 oC to 100 oC
  • Q mcDT 1Kg x 450 J/kg oC x 80 oC
  • 3.6 x 104 J

14
On the Stove
  • In heating 3.0 liters of water to make spaghetti
    Mikes stove heats water at a rate of 4500 watts.
    The initial temperature of the water is 150 C.
    After five minutes he sticks his hand in the
    water. Will he get scalded? What is the
    temperature?

DT Q/mc (4.5 x 103 x 300s)/(3.0kg x 4186 J/kg
oC)
107 degrees! What actually happened to the
water?
Started boiling when it reached 100 0C
15
Oops
  • A 145 g baseball crashes into a 500g pane of
    glass while moving at 30 m/s. The specific heat
    of the glass is 840 J/kg oC. Find the
    temperature increase of the glass assuming that
    half the balls KE is transformed into heating
    the glass.

KE ½ mbv2 0.5 x 0.145kg x (30)2 65.25 J
DT Q/mgc ½ KE/mgc (.5)(65.25)/(0.500kg x
840 J/kgoC)
0.078 degrees
16
Armageddon
  • An asteroid crashes into Earth while traveling 60
    km/sec. All its KE is transformed into heating a
    mass of rock (specific heat 860 J/kg 0C) equal to
    its own mass. What is the temperature increase
    of the rock? What happens to it?

½ mv2 mcDT
DT v2/2c
DT (6 x 104 m/s)2 / 2 x 860 J/kg 0C 2.1 x 106
0C
VAPORIZED BECOMES PLASMA
17
Calorimetry
  • When objects at different temperature are placed
    in thermal contact heat flows from the hotter to
    the cooler
  • Energy is conserved
  • Heat lost by one part of system heat gained by
    other part or parts
  • Calorimetry should be done in a container well
    insulated so that little heat is lost or gained
    from the outside. Sometimes it is necessary to
    include heat gained by Calorimeter cup.

18
Temperature of an Iron Block
  • 500g of iron is heated on a hot plate. It is
    placed in 200ml of water at 20 0C. After
    allowing time for thermal equilibrium to be
    reached the temperature of the water is found to
    be 500C. What was the initial temperature of the
    iron?

Heat lost by iron heat gained by water
Let TW be initial temp. of water TI that of
iron TF final temp of both
mIcI(TI-TF) mW cW (TF TW)
19
Temperature of an Iron Block, Continued
  • mIcITI mW cW (TF TW) mIcITF
  • TI mW cW (TF TW) mIcITF/ mIcI
  • TI 0.2 x 4186(50-20) 0.5 x 450 x 50/(0.5 x
    450)
  • TI 161 oC

20
Method of Mixtures
  • How can the specific heat of an unknown liquid
    such as antifreeze be determined? Design an
    experiment to do this.

21
Change of phase and Latent Heat
Courtesy Hyperphysics web site. Georgia State
University
22
Key Facts
  • Temperature does not change during change of
    phase
  • For water 00 C for freezing and melting
  • For water 1000 C for boiling and condensation
  • Slope during heating is related to specific heat!
  • Question compare the specific heat of ice with
    that of water.

That of ice is less
23
Q mL
  • Q is heat added or released
  • M is mass
  • L is latent heat
  • Heat of fusion solid to liquid or vica versa
  • Heat of vaporization liquid to vapor or vv
  • Table of Latent Heats
  • For water LF 333 kJ/kg 3.33 x 105 J/kg
  • LV 22.6 x 105 J/kg

24
Example
  • How much heat is required to turn 1 kg of ice at
  • - 200C to steam?
  • Heat the ice 1 x 2100 x 20 4.2 x 104 J
  • Melt the ice 1 x 3.33 x 105 3.33 x 105 J
  • Heat the water to boiling 1 x 4186 x 100 4.19
    x 105
  • Vaporize the water 1 x 22.6 x 105 22.6 x 105
    J
  • Total 3.05 x 106 J
  • How long would this take on a 4500 w burner?
  • Time Q/rate 3.05 x 106 / 4.5 x 103 678 sec
    11.3 min
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