To Come
l
Heat capacity (absorption)
u Specific heat
l
phase transitions
l
Heat and Work
l
1st law of
thermodynamics
l
heat transfer
u conduction
u convection
u radiation
l
Kinetic Theory of Gases
Heat and Temperature
So Far
l
Temperature vs Heat
l
Measuring temperature
l
Temperature scales and absolute zero
l
Thermal expansion
today
Expansion with Temperature
Molecular explanation:
u as temperature of solid increases, molecules move faster around average locations further from each other (expansion)
u High enough temp (kinetic energy), bonds holding atoms in lattice break (liquid), but forces still hold atoms nearby (not fixed
average location like solid) and more temp makes for greater separations (expansion)
u Raise temp even higher, bonds completely break --- gas --- more temp, more energy (expansion)
Solid Liquid Gas
review
Absolute Zero Temperature
l
Fixed amount of gas and fixed volume of bulb
l
find empirically pressure and temperature
proportional to each other
T = Cp
l extrapolate to lower temperatures
l all gases intercept at
T0=-273.15oC = absolute zero
review
Temperature Scales and Expansion
;
; L L T
A A T V V T
α
γ γ α
β β α
∆ = ∆
∆ ≡ ∆ =
∆ ≡ ∆ =
2 3
l Three temperature scales
l Mass of any system stays constant (until Relativitistic Quant Mech)
l Empirically as temperature increases, most materials increase their volume
l Coefficient of linear expansion, α (small)
review
Dangers - Diff Expansion
l
Pour boiling water into beaker - inside expands faster than outside
l
train tracks laid too close
together
Expansion Issues
l Expansion of solids creates difficulties
l Note real-life solution on bridges, ...
Special Case of Water
l Note ice density much smaller
u ρice=.917 g/cm3 …… phase change
l Lakes and ponds in winter: ice floats, insulates water below; warmest water at bottom
u Summer: water coolest at bottom
l Normal=
lsystem of fixed mass increases its volume when
temperature increases
lDensity normally decreases as T increases
lWater has peculiar property that
density increases below T=4oC
lWater at the
bottom of lakes is often at T=4oC even in winter
Heat Capacity
l System at top in equilibrium with environment
l System at bottom at lower
temperature. Heat energy, Q, will flow into system and
temperature will rise
l For fixed ∆T, amount of heat, Q depends on system type and mass
Q C T Q cm T
≡ ∆
≡ ∆
C = heat capacity c=specific heat
Note convention: heat added heat removed
Q Q
>
<
0 0
Specific Heats
l Measure of how much heat
energy it takes to raise unit mass one degree temperature
l Examples in table 19-3
l Note units and examples: water and copper or iron (more typical)
u cw=1 cal/g-oC = 1 Btu/lb-oF
u cw=4190 J/kg-K
u cCu=386 J/kg-K
u cFe=460 J/kg-K
l Molar specific heat multiplies by the number of kg in a mole =
.001 × molecular wt
u Note similar values-elements in table
u 1 mole has 6.02 1023molecules (see later)
Q ≡ cm T ∆
Again, notice
that water is
different!!
Heat changing temperature Sample prob 19-4
l Beaker: Cb Ti
l Water: mw Ti cw
l Copper: mc Tc cc
l Drop copper in water
l What is final temp, Tf?
l Intuitively, Ti < Tf < Tc
( )
( )
( ) ( )
( )
w w w f i
b b f i
c c c f c
w b c
c c c b w w i
f c c b w w
Q c m T T Q C T T
Q c m T T
Q Q Q
c m T C c m T
T c m C c m
= −
= −
= − <
+ + =
+ +
= + +
0 0
Cu
Q C T Q cm T
≡ ∆
≡ ∆
T
fChanging phases … heat required
l
To go from more ordered state to less ordered state requires adding energy
l
This added energy supplies the necessary potential energy of the bonding (or breaks the atomic bonds holding atoms together)
Solid Liquid Gas
Heat of transformation
l Materials can exist in different
“states” or phases. Typically
u Solid → liguid at T=melting point
u Liquid → gas at T=boiling point
u Example water
l Go from most ordered (solid) to least ordered (gas) as heat added
l Certain amount of heat required to change the state
u Heat of fusion, LF….solid to liquid
u Heat of vaporization, LV……liq to gas
l See table 19-4 in text for examples
u Most notable: WATER
o
L
F= 333 kJ/kg
o
L
v=2256 kJ/kg
can be or
F VQ mL
L L L
=
Gallium 30C
State or Phase Changes
Solid Liquid Gas
Motions Molecules of
l If forces holding
together a solid are more tightly bound, might expect
u Melting temp higher
u Expansion rate with temperature slower
l Correlation should exist!
Correlation
exists for
most metals
Heat changing the phase of water
l Water molecules vs ice molecules (avg locations)
l Behavior of 1 kg water vs temp
fusion vaporization
80 kcal 333 kJ
539 kcal
2256 kJ
0
0100
T (
oC)
Problem 46 (not assigned)
An insulated Thermos contains 130 cm
3of hot coffee, at a temperature of 80.0°C. You put in a 12.0 g ice cube at its melting point to cool the
coffee.
By how many degrees has your coffee cooled once the ice
has melted? Treat the coffee as though it were pure water and neglect energy transfers with the environment.
Ice
Back to Gases: Heat Doing Work … Work depends on how gas expands
dW F ds pA ds dW p dV
r r
=
=
• =
l Note that heat (Q ) supplied to gas has a portion (W ) doing work
l Work is area under p-V curve
l direction of process (sign W)
determines whether work done by or on the system
System of gas above: i→f
u insulated from outside world except reservoir
u reservoir supplies heat at rate determined by knob
u as piston on top rises, gas expands (& vice versa)
u Can vary pressure and volume (with temperature and weights)
First Law of Thermodynamics restricts the possibilities
l First Law of Thermodynamics = Energy Conservation
l Energy Conservation has three contributions
u W = work done (+) by system
u Q = thermal energy (+) added to system
u Eint = internal energy of system
u Eint is a consequence of the system
state (eg,could be function of P,V,T,…)
system = gas
Heat energy added to the system less the work done by the system equals the increase in system's internal energy
d E
i n t= d Q − d W
Example processes – see table 19-5
l
Adiabatic Q=0
l
Constant volume W=0
l
cyclical ∆E
int=0
l
free expansion Q=W=0
dE
int= dQ − dW
Sample Prob 19-5 work it through
int
kJ/kg
( )
f
i
f f
V
f i V
Q L m L
W p dV p V V
E Q W
= =
= = −
∆ = −
∫
2256
.
. .
.
in
Q kJ MJ
W J MJ
E Q W MJ
= =
= × =
∆ = −
=
5
2256 2 26 1 69 10 0 17 2 09
l 1 kg boiling water at 1
atmosphere (1.01 105 Pa)
l vol of water (10-3 m3)
changes to steam (1.671 m3)
l What changes & how much?
Processes and Cycles
l In the above processes, work is done, and the gas state might also change
u if Eint is different at i than at f
l Cycles are processes that return the gas to the starting point, have the gas end up in the same state as initially.
u Note that, even though the gas is in the same state, net work can be done in the cycle
u Some of the heat energy is converted to work
Problem 49 (not assigned)
A sample of gas expands from 1.0 m3 to 4.0 m3 while its pressure
decreases from 40 Pa to 10 Pa.
How much work is done by the gas if its pressure changes with volume via each of the three paths shown in the p-V
diagram in figure ?
A B C
W Joule
W Joules W Joules
=
=
=
120 75
30
Problem 51 (not assigned)
Gas within a closed chamber undergoes the cycle shown in the p-V diagram of Fig. 19-36 .
Calculate the net
energy added to the system as heat during one complete cycle.
Work done by system(positive) Work done on system
(negative)
No work done
Q=-30 Joules
(system lost heat)
Processes – return later
1.
Adiabatic Q=0
2.
Constant volume W=0
3.
cyclical ∆E
int=0
4.
free expansion Q=W=0
dE
int= dQ − dW = dQ − p d V
l
In chapters 20 and 21, we will discuss these more fully
l
Also use processes to understand
“ideal” and real gases
l
And to understand “entropy”
Heat Transfer
3 principal mechanisms
l
Conduction
u Heat transfer through material
u At microscopic level, thermal agitation of molecules causes adjacent molecules to also move more rapidly
l
Convection
u Occurs with fluids
u Has macroscopic cause: hotter fluid has
different (typically lower) density and moves up
l
Radiation
u NEW: completely different from those above
Heat and Temperature
So Far
l Temperature vs Heat
l Measuring temperature
l Temperature scales and absolute zero
l thermal expansion
l Heat capacity (absorption)
u Specific heat
l phase transitions
l Heat and Work
l 1st law of
thermodynamics
l heat transfer
To Come
l heat transfer
u conduction
u convection
u Radiation
u Processes and Cycles
l Kinetic Theory of Gases
u Where gas properties come from
u …
u Entropy …
