Temperature difference of `120^(@)C` is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length`(3L)/(2)`, is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to :

Options

A. `45^(@)C`
B. `60^(@)C`
C. `35^(@)C`
D. `75^(@)C`

Answer

A

Explanation

`R=(1)/(k)(L)/(A)`

`R_(eq)=(3R//2xxR)/(3R//2+R)+R=(3R)/(5)+R=(8R)/(5)`
`H=(120)/((8R//5))=(75)/(R),T_(P)=T_(A)-(75)/(R)((R)/(2))`
`T_(Q)=T_(B)+(75)/(R)((R)/(2)),T_(P)-T_(Q)=(T_(A)-T_(B))-75=120-75=45^(@)C`