Two lightbulbs have cylindrical filaments much greater in length than in diameter. The evacuated bulbs are identical except that one operates at a filament temperature of 2 1008C and the other operates at 2 0008C. (a) Find the ratio of the power emitted by the hotter lightbulb to that emitted by the cooler lightbulb. (b) With the bulbs operating at the same respective temperatures, the cooler lightbulb is to be altered by making its filament thicker so that it emits the same power as the hotter one. By what factor should the radius of this filament be increased

a

b

Explanation:

From the question we are told that

The filament temperature of the first bulb is

The filament temperature of the second bulb is

Generally according to Stefan-Boltzmann law the power emitted by first bulb is mathematically represented as

Here is the Stefan-Boltzmann with value

So

=>

Generally according to Stefan-Boltzmann law the power emitted by second bulb is mathematically represented as

=>

Given that the two bulbs are identical we have that

So

The ration is mathematically represented as

=>

Generally the area is mathematically represented as

Recall that

=>  

=>  

Now if the radius of the cooler bulb is increase by a factor Z (i.e Z * r )then the area of the cooler bulb

=>    

Here Z is the factor by which it is made thicker

So  For  

=>

0.11 m/s and 0.28 m/s should be correct

grav potential energy