James Joule and the mechanical equivalent of heat
• Joule knew a mass
above the ground had
potential energy. He
dropped an object on a
cord, turning a paddle
in water monitored by
a very accurate
thermometer.
• His conclusion was to
connect energy
conservation (potential
and kinetic) to heat as
a third form observed.
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Specific heat
• A specific heat value reveals
how much temperature will
change when a given amount of
a substance absorbs a given
amount of heat.
• Water is a “benchmark” as one
ml of water will absorb 1 cal of
heat to raise its temperature by
1oC.
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Symbols, signs, and definitions for heat and work
Hot coffee is poured into a room-temperature mug and over
time, they reach thermal equilibrium.
•
What is the sign of Q for the coffee?
•
Sign of Q for mug?
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Signs of heat and work on a system
Is the work W, the heat Q, and the change in thermal energy DEth, positive (+), negative
(-) or zero (0) for the following situations?
Does the temperature increase (+), decrease (-), or stay the same (0)
W
Q
DEth
DT
1.
You hit a nail with a hammer
2.
You hold a nail over a Bunsen burner
3.
You compress the air in a bicycle pump by pushing down on the handle very
rapidly
4.
You turn on a flame under a cylinder of gas, and the gas undergoes an isothermal
expansion
5.
A flame turns liquid water into steam
6.
High pressure steam spins a turbine
7.
Steam contacts a cold surface and condenses
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Does the path of the PV change matter?
• The start, the finish, and the shape of the curve are all significant.
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Compressed air
A compressed air cartridge at a starting pressure of p1 = 50 atm and
starting volume V1 = 5 cm3 is put into an empty, sealed balloon. It
pops and causes the balloon to expand to 10 times the volume of
the cartridge, V2.
• Assuming the air undergoes an isothermal expansion and behaves
like an ideal gas, draw the pV diagram of this process.
• What is the final pressure of the balloon p2?
• Two other ways different than the first method 1) of inflating the
balloon to the same final volume are 2) a constant pressure p1 = 50
atm inflates the balloon from V1 to V2 or 3) a constant pressure p2
(calculated above) inflates the balloon from V1 to V2. Draw pV
diagrams and rank the work done on the expanding air for the
three cases of expansion. E.g. W1>W2>W3
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Study of thermodynamic processes
• The cyclic process shown
proceeds counterclockwise
from a in the pV diagram to b
and back and the total work is
W = 500J.
• Why is the work positive?
• Find the change in thermal
energy and the heat added
during this process
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Thermodynamic process definitions
• Adiabatic
• Isochoric
• Isobaric
• Isothermal
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The processes on a PV diagram
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Adiabatic changes
• In an adiabatic process, no heat is transferred from system and
surroundings.
Adiabatic process a – b:
Q = 0, DEth = W
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Cyclic process
A cyclic thermodynamic process
occurs as shown, where path
c-b is isothermal. Draw
isotherms to determine
temperatures of states a, b, c.
Predict the Q, W and DEth for
each process:
What changes if c-b is adiabatic?
Q
W
a-c
c-b
b-a
Whole cycle
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DEth
Adiabatic and isothermal processes
Air (an diatomic gas with g = 1.4 ) at Pi = 1 atm
and Vi = 1m3 doubles its volume A) isothermally
and B) adiabatically
• Draw a PV diagram for both processes
• What is the final pressure for process A
and B?
• Compute W, DEth and Q for each
process.
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Measuring heat capacities
• Heat capacities may be
measured at constant volume
in a fairly complex process
using a bomb calorimeter.
• Heat capacities may be
measured at constant pressure
using equipment as simple as a
coffee cup.
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Relating heat capacities at constant volume and pressure
Q = DEth
Q = DEth - W
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Heat capacities tabulated for selected gasses
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Specific heat values
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Q17.3.5
You put 1 kg of the following materials on a bunsen
burner. Which one’s temperature rises the least?
A. Aluminum, c = 910 J/kg K
B. Berillium, c = 1970 J/kg K
C. Copper, c = 390 J/kg K
D. Water, c = 4190 J/kg K
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A17.3.5
You put 1 kg of the following materials on a bunsen
burner. Which one’s temperature rises the least?
A. Aluminum, c = 910 J/kg K
B. Berillium, c = 1970 J/kg K
C. Copper, c = 390 J/kg K
D. Water, c = 4190 J/kg K
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Water in a teapot
• A 500W heater dumps all its energy into heating 1kg of
water in a teapot. How long does it take to heat the water
to boiling if the water started out at room temperature?
• How many moles of water is this?
• cwater = 4190 J/kg K
• Mwater = 0.018 kg/mol
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Phase changes and temperature behavior
• A solid will absorb heat according to its heat
capacity, becoming a hotter solid.
• At the melting point, a solid will absorb its
heat of fusion and become a liquid. An
equilibrium mixture of a substance in both its
liquid and solid phases will have a constant
temperature.
• A cold liquid will absorb heat according to its
heat capacity to become a hotter liquid.
• At the boiling point, a liquid will absorb its
heat of vaporization and become a gas. An
equilibrium mixture of liquid and gas will have
a constant temperature.
• A cold gas can absorb heat according to its heat
capacity and become a hotter gas.
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Q17.4
You wish to increase the temperature of a 1.00-kg block
of a certain solid substance from 20°C to 25°C. (The
block remains solid as its temperature increases.) To
calculate the amount of heat required to do this, you
need to know
A. the specific heat of the substance.
B. the molar heat capacity of the
substance.
C. the heat of fusion of the substance.
D. the thermal conductivity of the
substance.
E. more than one of the above
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A17.4
You wish to increase the temperature of a 1.00-kg block
of a certain solid substance from 20°C to 25°C. (The
block remains solid as its temperature increases.) To
calculate the amount of heat required to do this, you
need to know
A. the specific heat of the substance.
B. the molar heat capacity of the
substance.
C. the heat of fusion of the substance.
D. the thermal conductivity of the
substance.
E. more than one of the above
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Hot pot
• A heavy copper pot of mass 2 kg is at temperature of 150C.
You pour 0.1 kg of water at 25C into the pot then quickly
close the lid so no steam can escape. Find the final
temperature of the pot and its contents and determine the
phase (liquid or gas) of the water. Assume no heat is lost to
the surroundings.
• cwater = 4190 J/kg K, ccopper = 390 J/kg K
• Lwater = 2256 x 103 J/kg
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Condensing steam
1671 cm3 of steam condenses to form 1 gram of water
(1 cm3) when held at a constant pressure of 1 atm
(1.013 x 105 Pa). The heat of vaporization at this
pressure is Lv = 2.256 x 106 J/kg.
1. Draw the pV diagram for this process
2. What is the work done by the water when it
condenses?
3. What is its change in thermal energy?
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Why, and how well, do materials transfer heat?
• Conduction: heat transfer
within a body or between
two bodies in contact.
• Convection: heat transfer
through movement of
mass from one place to
another
• Radiation: heat transfer
by electromagnetic
radiation
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Convection of heat
• Heating by moving large
amounts of hot fluid,
usually water or air.
• Figure 17.28 at right
illustrates heat moving by
convection.
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Conduction of heat I
• You bring a cooler to the
beach to keep some tasty
beverages cold. The
cooler has a total wall area
of 0.8 m2 and a wall
thickness of 2.0 cm. It is
filled with ice, water and
your tasty beverage at 0C.
What is the rate of heat
flow into the cooler if the
outside wall is at 30C?
• How much ice melts in 8
hours? Assume the same
rate of heat flow
calculated above.
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