Convection - Heat transfer in a gas or liquid by the circulation of currents from one region to...
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Transcript of Convection - Heat transfer in a gas or liquid by the circulation of currents from one region to...
Convection - Heat transfer in a gas or liquid by the circulation of currents from one region to another.Can be forced or spontaneous (natural).
Hot and cold liquid is brought in a thermal contact; it reduces the distance across which the conduction occurs and increases the contact area.
x
TkAH
Reducing heat-flow rate for better thermal insulation.
Thick (large x) cavities in house walls filled with insulating
(small k) materials;
Reducing the number of walls (small surface area A).
x
TkAH
Heat transfer by radiation. Stefan-Boltzmann law
4ATeP Total power, P [J/s=W], emitted by a hot object.
● 4th power of the absolute temperature, T.
● Surface area, A.
● Emissivity of the material, e.● Stefan-Boltzmann constant, )KW/(m107.5 428
Emissivity, e, varies between 1 (black body) and 0 (reflecting surface).
A good emitter of radiation (e ≈ 1) is also a good absorber. A radiator and a solar heater should be black.A thermos bottle should be silver-coated.
Emissivity, e, depends on the wavelength of the radiation.
For a solar heater, what values of e are the best for sunlight and for thermal waves radiated near 100 °C?
Gases
Gas is matter in a rarefied state.
The molecules are moving freely most of the time, and only once in a while undergo short-term collisions.
The macroscopic state of a gas in thermodynamic equilibrium is determined completely by its temperature, pressure, and volume.
The ideal gas law NkTPV P is the pressure, V is the volume, T is the absolute temperature…
N is the total number of molecules in the gas and
k is Boltzmann’s constant, k = 1.3810-23 J/K
The ideal gas law NkTPV
Gas in a cylinder under a piston
Pressure, P, is given by
AmgPP atm /Where m is the total mass of the
piston and the lead and A is the area of the piston.
We can:• add or remove the lead shots to change the pressure of the gas;
• tune the temperature of the thermal reservoir.
The ideal gas law PNkTV /Doubling the temperature, number of molecules, pressure?
Keeping the volume and the number of particles constant, but doubling the temperature?
VNkTP /
N is normally very big, while k is a very small number…
AnNN NA = 6.0221023 – Avogadro number, number
of molecules in 1 mol of a substance;
n is the number of moles in the gas.
nRTkTnNPV A R = 8.31 J/molK universal gas constant
Kinetic theory of the ideal gas
Kinetic energy is the only form of molecular energy that is important and it is preserved in the collision events.
L
reactionF
Collisions of the gas molecules with a wall..
As a result of a collision the momentum changes by
xx mvpp 22 Force due to one molecule as a function of time
Collisions of the gas molecules with a wall (cont.)
Newton’s second law for an instantaneous force: dt
dp
dt
dvmmaF xx
xx
Now t is a long time interval – the time between two consecutive collisions with the wall.
For the average force on the wall it becomes:
t
mv
t
pamF xxxx
2
reactionF
change of momentum in a collision
time between collisions
Now t is – the time between two consecutive collisions with the wall.
t
mvamF xxx 2
L
xvLt /2L
mv
vL
mv
t
mvF x
x
xxx
2
/2
22
Kinetic theory of the ideal gas.
L
vmNF x
2
L
vvvmF Nxxx )...( 22
221
N
vvvv Nxxxx
)...( 222
212
Let’s try to account for all molecules of the gas:
L
Kinetic theory of the ideal gas.
L
vNmF x
2
Pressure on the wall with surface area A:
V
vmN
LA
vmN
A
FP xx
22
Velocity of a molecule: ),,( zyx vvvv 2222
zyx vvvv
The average velocity – average of a sum is equal to the sum of averages…
2222zyx vvvv
All the directions of motion (x, y, z) are equally probable!
2222
3
1vvvv zyx
V – volume of the box.
L
Pressure on the wall with surface area A:
V
vmN
V
vmN
A
FP x
22
3
1
The average kinetic energy of a molecule
The ideal gas law (experimental fact!)
KNvmNPV3
2)
2
1(
3
2 2
2
2
1vmK
kTNPV
Therefore: KNNkT3
2 kTK
2
3