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 $
Engineering Growth Connection

STEFAN BOLTZMANN'S APPARATUS

1. OBJECTIVE:

To study the radiation heat transfer by black body and to study the effect of hemisphere
temperature on it.

2. AIM:

To calculate the stefan boltzmann constant.

3. INTRODUCTION:

All substances at all temperature emit thermal radiation. Thermal radiation is an

electromagnetic wave and does not require any material medium for propagation. All
bodies can emit radiation and have also the capacity to absorb all of a part of the radia-
tion coming from the surrounding towards it.

4. THEORY:

The most commonly used law of thermal radiation is the stefan boltzmann law which
states that thermal radiation heat flux or emissive power of a black surface is
proportional to the fourth power of absolute temperature of the surface and is given by

Q =Eb =aT 4 W/m 2 K4

A

The constant of proportionally is called the stefan boltzmann constant and has the value
of 5.67 x 1o·8 W/m 2 K4 . The stefan boltzmann law can be derived by integrating the
planck's law over the entire spectrum of wavelength from 0 to 00
• The objective of this
experimental set up is to measure the value of this constant fairly closely, by an easy
arrangement.

5. DESCRIPTION:

The apparatus consists of a hemisphere, fixed to a bakelite plate. Heater is provided to

give heat input to the water bath. Water bath is provided to heat the hemisphere. The
test disc is introduced at the center of hemisphere. The temperatures of hemispheres
and test disc are measured by given temperature sensors. Valves are provided for
supply and drainage of water.

K. C. Engineers Pvt. Limited, Ambala STEFAN BOLTZMANN'S APPARATUS

Page No. 1 of 6 (Rev. 1)
 Engineering Growth Connection

6. UTILITIES REQUIRED:

6.1 Electricity Supply: Single Phase, 220 V AC, 50 Hz, 5-15 Amp combined socket
with earth connection. Earth voltage should be less than 5 volts.

6.2 Water Supply (Initial fill).

6.3 Floor Drain Required.

6.4 Bench Area Required: 1.0 m x 0.5 m.

7. EXPERIMENTAL PROCEDURE:

7 .1 Sr ARTING PROCEDURE:

7.1.1 Close all the valves V1-V3.

th
7 .1.2 Fill heater tank 314 with water by removing the lid of the tank and put the
lid back to its position after doing so.

7.1.3 Ensure that switches given on the panel are at OFF position.

7 .1.4 Connect electric supply to the set up.

7 .1.5 Switch ON the mains ON/OFF switch.

7.1.6 Set the desired water temperature in the PIO by operating the increment
or decrement.

7 .1 .7 Switch ON the heater ON/OFF switch and wait till desired temperature
achieves.

7.1.8 Remove the disc from the bottom of test chamber by removing the support
provided to hold it.

7.1.9 Switch OFF the heater ON/OFF switch.

7 .1.10 Fill test chamber with hot water by opening the valve V 1 provided at top of
the chamber, till observing the overflow of water through chamber.

7.1.11 Close the valve V1.

7.1.12 Note the readings of water temperature and initial temperature of the disc.

7.1.13 Insert the disc to the bottom of the chamber and note the reading of
temperature after 5-10 sec interval.

K. C. Engineers Pvt. Umited, Ambala STEFAN BOLTZMANN'S APPARATUS

Page No. 2 of 6 (Rev. 1)
p:

7.2 CLOSING PROCEDURE:

*
Engineering Growth Connection

7.2.1 When experiment is over switch OFF the mains ON/OFF switch.

7.2.2 Switch OFF electric supply to the set up.

7.2.3 Drain the water bath and test section by opening the valveV2-V3.

8. OBSERVATION & CALCULATION:

8.1 DATA:

Mass of disc m = 0.007 kg

Diameter of disc D = 0.02 m
Specific heat of the disc material s = 418 J/kg°C

8.2 OBSERVATION TABLE:

T1= oc T4 = oc

oc Ts= oc
T2 =
oc Tsi = oc
T3 =
Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12
t (s) 5 10 15 20 25 30 35 40 45 50 55 60

T& (°C)

8.3 CALCULATIONS:

T=Tc+273.15 (K)

STEFAN BOLTZMANN'S APPARATUS

Page No. 3 of 6 (Rev. 1)
 Eng,neenng Growth Connection

CALCULATION TABLE:

S.No. t (s) T (K)

1
2
3

Plot the graph of T vs t and find the slope dT/dt.

ms(dT dt ) 2 4
u = ( 4 4 ) (Yv/m K )
Ao TE -To

9. NOMENCLATURE:

Norn Column Heading Units Type

Ao Area of disc mL Calculated

D Diameter of disc m Given

dT/dt Slope of the graph T vs t °C/s Calculated

m Mass of disc kg Given

s Specific heat of the disc material J/kg °C Given

T1 Temperature of enclosure oc Measured

oc Measured
Tti Initial temperature of the disc (Ambient Condition)
Temperature of disc at time t oc Measured
T,
T Temperature of disc at time t K Calculated

To Initial temperature of the disc K Calculated

TE Temperature of enclosure K Calculated

t Time s Measured

a Stefan boltzmann constant W/m£ K4 Calculated

10. PRECAUTION & MAINTENANCE INSTRUCTIONS:

10.1 Never run the apparatus if power supply is less than 200 volts and more than 230
volts.

10.2 Never switch ON mains power supply before ensuring that all the ON/OFF
switches given on the panel are at OFF position.

10.3 Operate selector switch of temperature indicator gently.

K C Engineers Pvt. Limited. Ambala STEFAN BOLTZMANN'S APPARATUS

Page No. 4 of 6 (Rev 1)
 m
Engineering Growth Connection

10.4 Always keep the apparatus free from dust.

11. TROUBLESHOOTING:

11.1 If electric panel is not showing the input on the mains light, check the main
supply.

12. REFERENCES:

th
12.1 Holman, J.P (2008). Heat Transfer. 9 Ed. ND: McGraw Hill. p 372.
rd
12.2 Cengel, Y.A (2007). Heat and Mass Transfer. 3 Ed. ND: Tata McGraw Hill. pp
28, 667-671.

C. Engineers Pvt. Limited, Ambala STEFAN BOLTZMANN'S APPARATUS

Page No. 5 of 6 (Rev. 1)