HEAT AND CALORIMETRY

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HEAT AND CALORIMETRY
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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

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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
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Joules Apparatus
Link to Joules original article
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Imagine This

• What other situations could be used to
  demonstrate the mechanical equivalent of heat?

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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?
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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
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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)

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Internal Energy Does Not Include KE

• KE of whole object represents all molecules
  moving in the same direction
• U is random motion only

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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
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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
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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.

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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

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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
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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
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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
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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.

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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)
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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

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Method of Mixtures

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

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Change of phase and Latent Heat
Courtesy Hyperphysics web site. Georgia State
University
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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
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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

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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