A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 
and power radiated by the wire is 94.2 W. Its emissivity is 
where 
_______ .
(Given 
and assume that the emissivity of wire material is same at all wavelength.)
Text Solution
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To determine the emissivity 
of the wire used in the bulb, we start with the given parameters and the formula for power radiated by a black body:
Length of the wire 
Diameter of the wire 
Temperature of the wire ( 
): 
Power radiated 
: 94.2 W
The power radiated by the wire can be expressed as:
Where:
is the Stefan-Boltzmann constant ( 
is the surface area of the wire, calculated using the formula for the surface area of a cylinder: 
Substituting the given values into the formula:
Simplifying the expression inside the parentheses:
On solving for 
:
Given that 
is 
, evaluating this expression provides the value of 
. Thus, the emissivity 
is 
.
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