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May I welcome you to our course Physical Chemistry. My name is Dr. Lauth.
Today we expect a task on
Thermal conductivity.
Thermal conductivity of conductive heat transfer -
without external current.
We need a temperature gradient (temperature gradient) for this kind of transport.
We need in our system
a change in the temperature with the location
If such a temperature gradient exists, can according to the first law of Fourier
the
Heat transport
calculate.
The relation
Heat flux density (dQ / (AdT))
is proportional
Felled the temperature (dT / dx).
The proportionality factor is called lambda
Thermal conductivity
The negative
Sign means that
the heat flux
downhill runs (from high temperature to low temperature)
This law can be in-patient
Heat conduction very well apply (here is dT / dx constant).
In unsteady heat conduction, the temperature gradient changed
(The temperature profile) - we need the second Fourier's law for more quantitative
Bills.
It is,
that the temperature change with time
a function of the curvature
the
Temperature profile is.
We consider this task a glass window
having dimensions of 1m x 1m and the thickness of 4 mm.
The outside temperature is 18 ° C,
the internal temperature is 20 ° C.
How much
Heat is transported?
We expect
We expect the temperature gradient -
the changes of temperature on a
Length of one meter from. To 4 mm
the temperature difference is 2 ° C, within a meter
(250 times)
the temperature change would be 250 times as large
this results in the
Temperature gradient to - 500 per meter Kelvin.
We use this gradient in
Fourier's equation
(That is multiplied by
minus 0.76 watts per meter Kelvin) and obtain
a heat flux of 380 W / m².
(Watts per square meter) - meaning per second go through our glass pane 380
Joule
from inside
outwardly.
We went when calculating a stationary
Temperature profile-
(Of a linear function Tt)
How can these 380 W / m²
lane?
Which figures are there?
If we assume
that we on average these
Have temperature gradients,
then correspond to the
380
Joules per second on an annualized basis
12 gigajoules
per square meter of window area.
When required by law
Minimum window area
for housing,
(12% -
12 m² to 100 m² apartment)
this corresponds to 1.44 gigajoules per square meter
and year.
Converted to comply
This 400 kilowatt hours per square meter.
400 kWh of heat loss through the windows alone
per square meter of living space.
This corresponds to
no contemporary
Insulation
and corresponds to a classification
in a
Heat demand category
worse than G
(Old, unrenovated buildings with single glazing)
A current
Standard is the low-energy house
with about one tenth of this thermal energy requirements.
A more efficient alternative
is the passive house with an annual heating energy demand
of less than 10 kilowatt hours per square meter.