Heat Transfer Experiment No.

Determination of Stefan Boltzmann constant

Name of the Student: Roll No:

Department of Mechanical Engineering Cummins College of Engineering for Women, Pune. Stefan Boltzmann Constant

Fig. 1: Schematic of experimental setup

Heat Transfer 1 Cummins College of Engineering Stefan Boltzmann Constant

Aim: To determine the value of Stefan Boltzmann constant

Introduction

The Stefan Boltzman’s law of radiation heat transfer states that the thermal radiation heat flux or emissive power of a black body is proportional to the fouth power of the absolute temperature. 4 Q = Eb(T ) = σ × A × T (1)

the constant of proportionality is called as Stefan Boltzmann constant and its values is σ = 5.67 × 10−8

Experimental Setup

The apparatus consits of flanged hemisphere fixed on nonconducting backelite plate. The outer surface of copper hemisphere is enclosed in a metallic water jacket. Water is heated in a small water tank with the help of the heater. The copper hemisphere is heated with the help of the hot water from this tank. The small copper disk is mounted on a backelite sleeve fitted in a hole drilled in the center of the base plate. The disk is covered with lamp black s as to act as black body. Four thermocouples are attached to the hemisphere at various locations to measure the mean temperature. The flat disc shaped black area element having its mass ‘m’ and specific heat Cp at temperature T5will start receiving heat by thermal radiation from the enclosure surface. The energy balance for the disk is written as shown in Eqn. (2)

dT 4 4 m · Cp · = σA(T − T ) (2) dt avg 1

Heat Transfer 2 Cummins College of Engineering Stefan Boltzmann Constant

Specifications

Hemisphere dia. 0.2 m Base Bakelite plate 0.3 m Test disc dia 0.02 m Thickness of test disc 0.002 m Mass of the test disk 0.007 kg Specific heat of the test disk material 380 J kg−1

Procedure

1. First boil the water in the water tank the help of immersion heater up to boiling temperature about 90 ◦C.

2. Then insert test disc in the backelite; if not inserted (test disc is blackened totally).

Record its temperature T1 and the hemisphere temperatures. i.e T2 to T5

3. Drop the boiled water on the hemisphere.

4. Record the temperarure of the test disk when it starts increasing; with the help of the stop watch after every 10 s. Till the steady state is reached i.e.5 consequent readings should indicate same temp.

Observation

Table 1: Temperature of the hemisphere

Sr.No Water Temperature Temperature of the hemisphere

T6 T1 T2 T3 T4

Heat Transfer 3 Cummins College of Engineering Stefan Boltzmann Constant

Table 2: Temperature of the test disk

Thermocouple Location Time in sec.

T5 5 10 30 . . . .. 60 .. .. 120

Calculations

From Eqn. (2) dT  m · Cp · dt σ = t=0 (3) 4 4 A · (Tavg − T5 ) Tavg is average temperature of hemisphere

Plot

Plot the temperature of the test disk against time and find out the slope of the curve at t =   0 as dT dt t=0

Conclusion

Value of Stefan Boltzman constant is from the above experiment is The difference between the actual and experimental value is due to following reasons,

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Heat Transfer 4 Cummins College of Engineering