CHEMICAL ENGINEERING GROUP
STEFAN BOLTZMANN APPARATUS
STEFAN’S BOLTZMANN APPARATUS 1
CHEMICAL ENGINEERING GROUP
STEFAN BOLTZMANN APPARATUS
OBJECTIVE
Study of Radiation heat transfer by black body.
AIM
To determine Stefan Boltzmann constant.
THEORY
All substances at all temperature emit thermal radiation. Thermal radiation is an
electromagnetic wave and does not require any material medium for propagation. Radiation
that is emitted by the surface originates from the thermal energy of matter bounded to the
surface. The rate at which energy is released per unit area is termed as surface emissive
power.
There is an upper limit to the emissive power prescribed by Stefan-Boltzmann law. This law
states that emissive power of a black body is proportional to the fourth power of absolute
temperature of the surface and is given by
E b σTs4
The constant of proportionally is called the Stefan Boltzmann constant and has the value of
5.67 x 10-8 W/m2 K4. The Stefan Boltzmann law can be derived by integrating the Planck’s
law over the entire spectrum of wavelength from 0 to .
DESCRIPTION OF APPARATUS
The apparatus consists of a copper disc is centered on a flanged copper hemispherical
enclosure fixed on a flat non-conducting base plate. The disc, which is mounted in an
insulating bakelite sleeves is fitted in a hole drilled in the centre of the base plate. The outer
surface of hemisphere is enclosed in a water jacket. Circulating water from a supply tank
passes through the jacket and is used to maintain the hemisphere surface at some desired
temperature. A heater in the supply tank facilitates variation of water temperature.
STEFAN’S BOLTZMANN APPARATUS 2
CHEMICAL ENGINEERING GROUP
The hemisphere temperature is measured using a temperature sensor and the same is
read by a temperature indicator. Another temperature sensor is used to measure the
temperature of disc. The inner surface of hemisphere, base plate forming the enclosure and
the surface of the copper disk are coated using lamp black to approximate a black body.
UTILITIES REQUIRED
Electricity Supply: 1 Phase, 220 V AC, 2 Amps.
EXPERIMENTAL PROCEDURE
1. Note ambient temperature and pressure before commencing measurements.
2. Ensure that there is water in the supply tank before starting main power supply.
Switching the heater on with no water in the tank will lead to overheating and damage
the heater.
3. Ensure that the disk is not in position and detached from base plate at the start of the
experiment.
4. Ensure that the valve on the overflow line is open.
5. Switch on the main power supply to the test set-up and heater.
6. Set the water temperature in the supply tank to some desired temperature.
7. Once the water is the supply tank attains the desired temperature, start flow of water
through the jacket.
8. The hemispherical enclosure and the base plate will attain some uniform temperature
in a short time after the hot water fills the jacket. The jacket is considered completely
filled when water starts to flow from the overflow line provided. The thermal inertia of
hot water is quite adequate to prevent significant cooling in the time required to conduct
the experiment.
9. Close the valve on the overflow line. Allow the enclosure to attain thermal equilibrium.
Note the steady state temperature of the enclosure.
10. Note down the temperature of the disc before inserting in the base plate (at time t = 0)
11. Insert the disk into the base plate and note the temperature change every five seconds
for duration of three minutes.
12. To conclude the experiment, detach the disk first. Switch of the heater in the supply tank.
Allow the water in the hemisphere to cool before draining it off. Consult the lab
instructor before doing this.
STEFAN’S BOLTZMANN APPARATUS 3
CHEMICAL ENGINEERING GROUP
SPECIFICATIONS / KNOWN DATA
Hemispherical enclosure diameter : 200 mm
Base plate diameter : 250 mm
Test disc diameter : 20 mm
Mass of test disc : 5.1 g
Specific heat of the disc : 418 J/kg.K
OBSERVATIONS
1. Temperature of enclosure: _______ºC
2. Temperature of disc (at t = 0): _______ºC
Time / sec Disk temperature / ºC
5
10
15
20
.
.
.
Till 120 or 180 seconds
DATA REDUCTION
Area of the disc (m2)
The cross sectional area AD of the disc is evaluated using
d2
AD
4
Stefan Boltzmann constant (W/m2.K4)
The Stefan Boltzmann constant is calculated from
STEFAN’S BOLTZMANN APPARATUS 4
CHEMICAL ENGINEERING GROUP
dT
mcP
dt t 0
σ
AD (Th4 TD4 )
where cP denoted the specific heat of the disc material and Td denoted the thermodynamic
temperature of the disk at time t = 0
NOMENCLATURE
AD Area of disc
th Temperature of hemisphere enclosure in Celsius
Th Thermodynamic temperature of hemisphere enclosure
TD Thermodynamic temperature of disc at time t = 0
m Mass of disc
cP specific heat of the disc material
σ Stefan Boltzmann constant
Precautions & Maintenance Instructions:
1. Always use clean water. Ensure that the heater is submerged in water before switching
ON the heater.
2. Always note the temperature of the disc before attaching it to the base plate.
3. Use stabilized A.C. Single Phase supply only.
4. Never switch on mains power supply before ensuring that all the ON/OFF switches
given on the panel are at OFF position.
5. Voltage supply to heater should be constant.
6. Never run the apparatus if power supply is less than 180 V and above than 240 V.
7. Operate selector switch of temperature indicator gently.
8. Always keep the apparatus free from dust.
9. Don’t switch ON the heater before filling the water into the bath.
REFERENCES:
1. Holman, J.P., Heat Transfer, 9th edition, McGraw Hill, NY, 2004
2. Incropera, F. P. and Dewitt, D. P., Heat and Mass transfer, 5th Edition, 2002
STEFAN’S BOLTZMANN APPARATUS 5
