Determination of Stefan Boltzmann's Constant

Aim

To determine the value of Stefan Boltzmann's constant.

Specifications:

Hemispherical enclosure diameter - 200 mm

Size of water jacket for hemisphere- 260 mm

Base Plate, hylum diameter - 240 mm

Test disc diameter - 20 mm

Specific heat of test disc (Cp)- 0.4168 kJ/kg K

No. of thermocouples mounted of enclosure - 4

No. of thermocouples mounted on the disc- 1

No. of thermocouples mounted water heater - 1

Immersion water heating capacity - 2000 watts

Mass of test disc - 0.008 kg

Apparatus Required:

• Experimental setup for Stefan Boltzmann's constant determination, with heater arrangement.
• Stabilized power Supply
• Stop Clock

Procedure:

1. Switch on the power supply and set an input voltage (65 V) using the Voltage regulator.
2. Fill the Stainless Steel cubical vessel with 7 litres of water and heat the water to 80°C.
3. Open the Values & allow the hot water to fill the chamber
4. Allow the hot water to stabilize for 10 minutes & measure the temperature of the chamber and three different locations on the inner hemispherical surface.
5. Measure temperature of test surface to evenly 10 secs until it reaches a steady state
6. Calculate the Stefan Boltzmann's constant by applying Stefan Boltzmann’s law.

Observations:

Temperature of hot water T₁= 80°C

Observation of disc temperature (T₅):

Formula Used

Emissive power (E) = σ A_DT _S⁴

Where,

A_D = Area of the disc ‘D’ in m ²

T_S = Average surface temp of Enclosure = T₂+T₃+T₄in K/3

The radiant energy of the disc D, emitting into the enclosure E_D is

E_D = σ A_DT_D⁴ = σ A_D(T_avg⁴-T_d⁴)

Where,

T_D = Temperature of disc T₅in K

The net energy transferred to the disc

m_cpdT/dt= σ A_D(T_D⁴ -T_s⁴)

Where,

m - Mass rate of test disc in kg

Cp - Specific heat of test disc in kJ/kg K

Stefan Boltzmann's Constant (σ) = m C_p(dT/dt)/A_D(T_D⁴ -T_s⁴) W/m²K⁴

Model graph :

Result:

Thus the Stefan Boltzmann's constant is determined as (σ) .............

Viva-Voce Questions

State Stephan Boltzmann law & its constant value?

The emissive power of a black body is proportional to fourth power of its absolute temperature & its constant’s value is 5.67x10-8 W/m2 K4

What is the effect on internal energy of an object during radiation?

In radiation, internal energy of an object decreases.

Define Emissive Power

It is defined as the total amount of radiation emitted by the body per unit time and unit area.

Define Monochromatic emissive Power

The energy emitted by the surface at a given length per unit time per unit area in all dimensions is known as monochromatic emissive power.

Define Radiation

The heat transfer from one body to another without any transmitting medium is known as radiation

Define Emissivity

It is defined as the ability of the surface of a body to radiate the heat.

What is meant by Gray body?

If a body absorbs a definite percentage of incident radiation irrespective of their wavelength, the body is known as Gray body.