The figure shows the tungsten filament with constant diameter except a piece of it which has half the diameter of the resy of the wire. Assume the the temperature is constant with in each part and charges suddenly between the parts. If the temperature of thick part is 2000 K, the temperature of the thin part of the filament is

Options

A. 2000 K
B. `2^(1//4)(2000)K`
C. `8^(1//4)(2000)K`
D. `4^(1//2)(2000)K`

Answer

C

Explanation

In steady state
`I^(2) R = sigma T^(4) xx` surface area
`I^(2)rho(l)/(pir^(2))=sigmaT^(2)2 pi rl`
`rArr T^(4) prop (1)/(r^(3))rArr (T_(1))/(T_(2))=((r_(2))/(r_(1)))^(3//4)`