Download Heat Heat Capacity Latent Heat Latent Heat

Heat
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Heat Capacity
What is heat?
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Heat (Q) is the “flow” or “transfer” of energy from
one system to another
Often referred to as “heat flow” or “heat transfer”
Requires that one system must be at a higher
temperature than the other
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Heat will only flow from the system with the higher
temperature to the system with the lower temperature
Heat will only flow from the system with the higher average
internal energy to the system with the lower average
internal energy
Total internal energy does not matter.
Latent Heat
Heat capacity connects heat flow to temperature change:
Q = CΔT
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Heat capacity C depends on material, and also on the quantity of
material present. Eliminate quantity dependence by introducing
specific heat c and molar heat capacity c′:
Q = mcΔT
m = mass
Q = nc′ΔT
n = number of moles
Latent Heat
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A phase change occurs when a solid melts to a liquid, a liquid boils to
a gas, a gas condenses to a liquid, and a liquid freezes to a solid.
‰ Each of these phase changes requires a certain amount of heat,
although the temperature does not change.
‰ If a solid becomes liquid, or vice versa, the amount of heat per gram is
the latent heat of fusion.
‰ If a liquid becomes gas, or vice versa, the amount of heat per gram is
the latent heat of vaporization
A glass is filled with 100 g of ice at 0.00°C and 200 g of water at 25.0°C.
(a) Characterize the content of the glass after equilibrium has been
reached. Neglect heat transfer to and from the environment. (b) Repeat
your calculations for 50.0 g of ice and 250 g of water.
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Work
Work Done by Thermal Systems
Work can be done by thermal systems, as
in the expansion of a gas.
Using the definitions of work and pressure:
G G
dW = F • ds = PAds
V
W = ∫V 2 PdV
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Note, work can be done on a thermal
system, as in the compression of a gas.
First Law of Thermodynamics
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When temperature changes, internal energy has changed –
may happen through heat transfer or through mechanical work
First law is a statement of conservation of energy
Change in internal energy of system equals the difference
between the heat added to the system and the work done by the
system
ΔU = Q − W
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dU = dQ − dW
Differential form
Heat added +, heat lost -, work done by system +, work done on system –
Internal Energy U is a state property
Work W and heat Q are not
But work and heat are involved in thermodynamic processes that change
the state of the system
Types of Transformations
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Isobaric, ΔP = 0
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W = PΔV
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Work = Pressure*Change in Vol
W = ∫V B PdV =P ∫V B dV =P(VB − VA )
V
A
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V
A
ΔU calculated from 1st law
Isochoric, ΔV = 0
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W = 0 ⇒ ΔU = Q
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The change in internal energy of
the system equals the heat added
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The PV diagram shows two states of a system containing
1.45 moles of an ideal gas
(P1 = P2 = 450
N/m2, V1 = 2.00 m3, V2 = 8.00 m3).
A) Draw an isobaric process from state 1 to state 2.
B) Draw a two-step process that depicts and isothermal
expansion from state 1 to V2 followed by an isochoric
increase in temperature to state 2.
C) In both cases, calculate the work done, the heat added
or lost, and the change in internal energy.
Types of Transformations
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Isothermal, ΔT = 0
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ΔU = 0, ⇒ W = Q
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Work done by the system equals
the heat added to the system
V
V
W = ∫V B PdV = ∫V B
A
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A
⎛V ⎞
nRT
dV =nRT ln⎜⎜ B ⎟⎟
V
⎝ VA ⎠
Adiabatic, Q = 0
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⇒ ΔU = -W
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Work done by the system lowers
the internal energy of the system
by an equal amount
Temperature can change only if
work is done.
Molar Specific Heats for Gasses
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Molar specific heats for gasses are
different if heat is added at constant
pressure vs constant volume
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QP = nCPΔT
QV = nCVΔT
Isobaric, ΔP = 0
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Equipartition of Energy
W = PΔV
QP = ΔU + PΔV
Isochoric, ΔV = 0
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W = 0 ⇒ QV = ΔU
If the two processes result
in the same temperature
change, ΔU is the same.
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Diatomic, triatomic, etc. molecules are more complex
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Molecules can translate, rotate, and vibrate
Energy is shared equally between the various degrees of freedom
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A certain gas has a specific heat cV = 0.0356 kcal/kg-oC, which changes little over
a wide temperature range. What is the atomic mass of the gas? What gas is it?
Adiabatic, Q = 0
Assume an adiabatic and quasistatic
expansion of an ideal gas.
dU = − dW = − PdV
After a lot of calculus and algebra (see p 592):
PV γ = constant, where γ =
CP
CV
For the same increase in volume, an adiabatic process will result in a
lower pressure and lower temperature than an isothermal process.
What about work?
Wadiabatic =
Heat Transfer
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Results from molecular
interactions
„ Collisions?
Energy is transferred through
interaction
Results from the mass transfer of
material
Think fluid flow
Radiation
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Energy transferred by
electromagnetic radiation (waves)
Does not require a “medium”
The material
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Will Review in
Lec 3-6
Will Review in
Lec 3-6
Time rate of heat transfer depends on
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Convection
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⎛V ⎞
Wisothermal = nRT ln⎜⎜ B ⎟⎟
⎝ VA ⎠
Conduction
Conduction
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P1V1 − P2V2
1− γ
Specifically k = thermal conductivity
Area
Temperature difference
Thickness or length
ΔQ
T −T
= kA 2 1
Δt
l
Differential form
dQ
dT
= −kA
dt
dx
R-Value, Thermal Resistance Value
R=
l
k
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Your refrigerator can be thought of as a box with six sides of total area 2.5 m2. The
effective R value of the walls is 1.5 m2–K/W. The temperature inside is 5.0°C,
while the temperature outside is 25°C. Calculate the rate of heat loss.
Radiation
Time rate of heat transfer depends on
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The material
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Area
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Temperature difference
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Will Review in
Lec 3-6
Specifically e = emissivity
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Surface area
Did Not Cover.
Will be covered
in Lec 3-6
Experimentally determined to be proportional to the 4th power of T
An experimentally determined Stefan-Blotzmann constant σ
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ΔQ
= eσAT 4
Δt
0 ≤ e ≤1
σ = 5.67 ×10 −8 W / m 2 ⋅ K 4
A surface that is “white hot” emits about 10 times more power than a “red hot”
surface. What does this tell us quantitatively about the relative temperature?
(
ΔQ
4
= eσA T1 − T24
Δt
)
Did Not Cover.
Will be covered
in Lec 3-6
Objects that become sufficiently hot will glow visibly; as they get
hotter they go from red, to yellow, to a bluish white.
This is electromagnetic radiation; objects at any temperature will
emit it at various frequencies, from radio waves all the way to
gamma rays.
This radiation from a body in thermal equilibrium is called blackbody
radiation, as it is purely thermal and doesn’t depend on any
properties of the body other than its temperature and area.
Deriving the energy density as a function of frequency and
temperature required introducing some new concepts:
Blackbody Radiation
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Did Not Cover.
Will be covered
in Lec 3-6
Net heat flow between
two objects
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Here, c is the speed of light:
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And h is Planck’s constant:
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