Rate in Thermal
Systems
Overview
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Fundamental Concepts
•
What is the prime mover in the
thermal system?
–
•
What does rate measure in the
thermal system?
–
•
temperature difference ( T)
heat flow (QH)
How does heat flow?
–
from areas of high temp to low temp
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Heat Flow
• Why does heat flow?
– molecules with high temperature vibrate faster
than molecules at lower temperature – more
kinetic energy
– when the molecules bump into one another,
energy is transferred from the high energy
molecule to the low energy molecule
– this continues until all the molecules have equal
energy levels
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Heat vs Temperature?
• What is heat?
– Heat is a form of energy relating to the
vibrating motion of atoms and molecules
• What is temperature?
– Temperature is a measure of the
average kinetic energy of the molecules
of a substance
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Calculation of Heat Flow (QH)
• How do we calculate heat flow?
– Heat Flow = Heat energy
transferred/elapsed time
– Quantity of heat = amount of heat
energy moved per unit time
– QH = H/t
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Units of Heat Flow - Metric
• What are the units for heat flow?
– any unit of heat / any unit of time
– common units – J/s; cal/s; Btu/hr
• What is a calorie?
– amount of heat required to raise the
temperature of one gram of water one
degree Celsius;
– Often a kilocalorie = 1000 cal is used
– SI (metric) unit of heat flow
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Units of Heat Flow - British
• What is a Btu?
– British thermal unit
– amount of heat required to raise
the temperature of one pound of
water one degree Fahrenheit
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Specific Heat
• What is specific heat?
– every substance has a unique specific heat
– it is a fixed quantity and is the amount of
heat required to raise one gram of a
specific substance by one degree Celsius
– used to determine the amount of heat
required to change the temperature of a
mass of a substance
– Symbol is c
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Calculation of Heat Energy
• What is the equation for
calculating heat energy during a
temperature change?
– H = (m)(c)( T), where
• H = amount of heat
• m = mass of sample
• c = specific heat of substance, and
T = Final temp – initial temp
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Example - Specific Heat Calculations
• What is the specific heat of water?
– 1 cal/gm-oC or 1 Btu/lb-oF
• Example – How much heat is required to
heat 417 pounds of water from 70oF to
130oF?
–
–
–
–
H = (m)(c)( T)
H = (417 lbs)(1 Btu/lb-oF)(130-70)
H = (417)(1)(60)
H = 25,020 Btu
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Heat Exchange - Hot to Cold
• Suppose you heat a metal ball and
place it in a cup of cold water. How
does the heat flow?
– heat will flow from the ball to the water
– the amount of heat lost by the metal is
equal to the amount of heat gained by
the water
• This is an example of conservation
of energy
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Example of Heat Exchange
• Example – A 25kg brass ball at 100C
is placed in a container of water at
10C. When the brass-water system
has stabilized the final temperature
is 30C.
– How much heat (H) was removed from
the brass ball and added to the water?
(c for brass = 0.091 kcal/C˚)
– What is the mass of water in the
container?
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Calculations of Heat Transfer
• Part 1
– H = mc T
– H = 25 (0.091)(100-30)
– H = 159.3 kcal = 159,300 cals
• Part 2 – heat lost by ball was added to water
– H = mc T
– 159,300 = m(1)(30-10)
– 159,300 = 20m
– m = 159300/20
– m = 7965 gm
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Heat Flow Rating
• An air conditioner is rated at
10,000 Btu.
– What does this mean?
• The unit can remove heat at a rate of
10,000 Btu per hour
• This removal of heat will cause a
change in temperature
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Calculation of Heat Flow Rating
• Example – A 5000 Btu heater runs for
5 hours and 30 minutes.
– How much (what quantity of) heat is
moved?
• QH = H/t
• 5000 Btu/hr = H/5.5 hrs
• H = 27,500 Btu
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Heat flow Rate & Thermal Conductivity
• What factors affect
the heat flow rate (QH)
across a material of
thickness (l), temp
difference ( T), area
(A) and thermal
conductivity (k)?
– QH = kA T/l, where
• QH is measured in units
such as Btu/hr, or cal/sec
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Thermal Conductivity Examples
• Examples of thermal conductivity, in
British units, are:
– Air = 5.7 x 10-4
– Corkboard = 0.30
– Aluminum = 1400
Heat Amount vs Heat Flow Rate
• H = The amount of heat that can be
added to or removed from a body
• QH = the rate of heat flow through a
material due to a temperature
difference across the material, for
example:
– Inner and outer walls on a house,
– ski jacket, etc
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Change of State
• What is a change of state?
– changing a substance from a solid
to a liquid or a gas
– Solid-liquid = melt
– Liquid-gas = vaporize
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Types of Heat
• What is sensible heat?
– Applied heat that changes the
temperature of a substance
• What is latent heat?
– Applied heat that does not change the
temperature of a substance
– the applied heat causes the substance
to change state (from a solid to liquid)
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Latent Heat Schematic
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Rate in the Thermal System
• Example – A sample of ice at -10oC is
heated until it becomes steam at 110oC.
– Classify the heat changes as latent or
sensible.
– -10oC ice to 0oC ice  sensible
– 0oC ice to 0oC water  latent
– 0oC water to 100oC water  sensible
– 100oC water to 100oC steam  latent
– 100oC steam to 110oC steam  sensible
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Temperature measuring devices
• Thermometers
– Celsius (C)
– Fahrenheit (F)
• Thermocouples
– The temperature of the junction of
2 different metals translates to
voltage
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