-
-
--------------------- 2563 - TEMPERATURE - Getting Temperature from Light?
-
- We have leaned that atoms have orbiting electrons at distinct orbits, only those orbits having a standing wave, or multiple of a standing wave circumference. A standing wave is a wave of half wavelengths where the end points are held stationary.
-
- Other orbits are not allowed otherwise a moving electron radiates energy. If an electron in an atom absorbs or emits energy it must jump between these predefined orbits. It must always absorb or emit a quantum of Energy / frequency equal to Planck’s
-
----------------------------- Constant of Action = 6.6*10^-34.
-
----------------------------- Energy / frequency = a constant. E = h*f.
-
- So, if we measure the frequency emitted we know the energy gap between orbits for that particular atom. And , if we know the energy gaps for each element we can measure the frequency of radiation and identify the element that created. it. That is how astronomers know the makeup of stars and gas nebulae that are billions of light years away. But, how do we measure temperature from this same data?
-
- It is Boltzman’s Constant that provides a bridge between temperature and energy. Ludwig Boltzman worked on statistical physics in the 1850”s and in 1884 he wrote the thermo dynamic equations for radiated power. In 1879 Josef Stefan discovered experimentally that radiated power, which is energy per unit time, per unit area varies as the 4th power of temperature.
-
-------------------- Boltzman later proved it mathematically.
------------------- Radiated Power = 5.68*10^-8 * temperature^4 watts / (meters^2*K^4)
-
------------------- Radiated Power / temperature^4 = a constant
-
- The Stefan-Boltzman constant is a small number 0.000000057 watts/(m^2*K^4)
If the temperature increase the radiated power must increase a lot in order to the keep the ratio a constant.
-
- One mole is the mass in grams equal to the element’s atomic weight. One mole contains 6*10^23 molecules. This is known as Avagadro’s Number. A cube of sugar contains 600,000,000,000,000,000,000,000 molecules of sugar.
-
- At a constant temperature the pressure * volume / number of molecules = a constant. At a constant temperature if pressure or volume increase number of molecules in that volume must increase.
-
----------- Pressure * Volume = n* R* Temperature
-
------------ n*R is a constant = 8.3 Joules / mole*Kelvin
-
------------ p*v / n*T = 8.3
-
------------- where little “n” is the number of molecules
-
- The product of pressure and volume to number of molecules and temperature is a constant 8.3. If temperature increases the pressure and volume must increase. If pressure increases and the temperature remains constant then volume must decrease. If pressure increase and volume is constant then temperature must increase.
-
------------ Boltzman’s Constant = K = 1.381*10^-23 Joules / Kelvin
-
- If we plot the radiated power versus frequency we find that power increases with frequency up to a maximum and then it decreases back to a minimum. This is known as the Blackbody Curve. The maximum power occurs at the frequency where h * f = K*T
-
----------. Planck’s Constant * frequency = Boltzman’s Constant * Temperature.
-
----------- h * f = K * T
-
----------- h = 6.6*10^-34 joule*seconds.
-
------------ K = 1.4*10^-23 joules/Kelvin
-
------------ f / T = 1.4*10^-23 / 6.6*10^-34 = 22,00,000,000 cycles/second*Kelvin
-
- The ratio of frequency to Temperature is a constant, 20,800,000,000. The constant is a big number. If temperature increase the frequency increases. Astronomers mostly deal in wavelengths instead of frequency, so we can translate this equation into wavelengths.
-
-------------- Frequency * Wavelength = speed of light
-
---------------- f * w = c = 300,000,000 meters per second
---------------- T * w = 0.0029 meter*Kelvin
-
- The product of Temperature and Wavelength is a constant 0.0029. If temperatures increase the wavelength decreases, smaller wavelengths means a higher temperatures. That is why a hotter flame turns from red to yellow to blue as it gets hotter.
-
- The wavelength versus radiation power graph of a Blackbody emitting or absorbing radiation is always the same shape. The maximum and the minimums shift but the shape is always the same. The Sun is a perfect emitter and considered a Blackbody. The maximum intensity of the Sun occurs at frequency of 6.2*10^14 cycles per second. This is a wavelength of 4.8*10^-7 meters, or 480 nanometers. T * w = 0.0029, therefore the temperature is 6000 K.
-
- The core of the Sun is very dense, containing 10^26 particles per cubic centimeter. The temperature is `15,000,000 Kelvin. Compare the pressure at the core with the pressure at the surface of the Earth, which is at 1 atmosphere. Pressure is the force per unit area exerted on any surface. Pressure depends of the number density of particles.
-
-------------------- Pressure = n * k * T
-
--------------------- “n” Sun = 10^26
-
--------------------- K = 1.4*10^-23 joules/Kelvin
-
------------------ Pressure Sun core / Pressure Earth = n*k*T Sun / n*k*T Earth
-
------------------- n*Tsun / n*T earth = 10^26 * 1.5*10^7 / 2.4*10^19 * 300
-
----------------- where the at the surface of the Earth the density is 2.4*10^19 molecules per cubic centimeter and the temperature is 300 Kelvin.
-
- ------------------------------- pS / pE = 200,000,000,000
-
- The pressure at the core of the Sun is 200 billion times greater then the pressure at the surface of the Earth. No wonder a thermo nuclear fusion reaction occurs at the core of the Sun. And, no wonder it is so hard to create a fusion energy power source here on the surface of the Earth.
-
--------------------------------------------
-
(1) -------------------- Planck’s Constant of Action = h = 6.260755
-
(2)) -------------------- Boltzman’s Constant = K = 1.380658 joule / Kelvin
-
(3)) -------------------- Avagadro’s Number N = 6.0221367 * 10^23 molecules / mole
-
(4)) -------------------- Speed of Light = c = 299,792,458 meters per second
-
(5) ) -------------------- Wein Displacement Constant = 0.002897756 meters*Kelvin
-
(6) ) -------------------- Molar gas Constant = R 8.314510 joule / (mol*Kelvin)
(7)) -------------------- Stefan-Boltzman Constant = 5.67051*10^-8 watts / (m^2*K^4)
-
- Other Reviews on this subject:
-
- Review 505 How small is the Atom”
-
- Review 983 - “How an Atom Works”
-
- Review 985 - “Measuring How an Atom Works“.
-
- Review 986 - “How a Molecule Works“.
-
- Review 924 - “Rutherford’s Atom”
-
- Review 1740 - “Temperature of the Earth”
-
- Review 2377 - “Defining the Atom”
-
- Review 2333 - “Rainbows can Tell Us What the Universe is Made Of.”
-
- Review 2555 - History of the Atom to 1925
-
- Review 2555 - History of the atom after 1925
-
- December 24, 2019. 2563 988
----------------------------------------------------------------------------------------
----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
- https://plus.google.com/u/0/ -- www.facebook.com -- www.twitter.com
--------------------- Thursday, December 26, 2019 -------------------------
-----------------------------------------------------------------------------------------
No comments:
Post a Comment