A copper strip `AB` and an iron strip `AC` are joined at `A`. The junction `A` is maintained at `0^@ C` and the free ends `B and C` are maintained at `100^@ C`. There is a potential difference between

Options

A. 0.78 mm
B. 0.90 mm
C. 1.56 mm
D. 2.34 mm

Answer

A

Explanation

Rate of the flow from Q to P `(dQ)/(dt)=(2KA(T-10))/(1)`
Rate of heat flow S to R `(dQ)/(dt)=(KA(400-T))/(1)`
At steady state rate of heat flow is same :

`therefore(2KA(T-10))/(1)=(KA(400-T)or2T-20=400-T`
or `3T=420thereforeT=140^(@)C`
Temperature of junction is 140°C
Temperature at a distance x from end P is `T_(X)=(130X+10^(@))`
`[Use(KA)/(1)(140-10)=(KA)/(X)(T_(X)-10)]`
Change in length dx is suppose dy

Then `dY=alphadx(T_(X)-10)`
`int_(0)^(DeltaY)dY=int_(0)^(1)alphadx(130X+10-10)`
`DeltaY=[(alphax^(2))/(2)xx130]_(0)^(1),DeltaY=1.2xx10^(-5)xx65,DeltaY=78.0xx10^(-5)m=0.78mm`