Two plates of equal area are placed in contact with each other. The thickness of the plates are 2.0 cm and 3.0 cm respectively. The outer face of first plate is at `-25^(@) C` and that of second plate is at `+25^(@) C`. The conductivities of the plates are in the ratio `2:3`. Calculate the temperature of the common surface of the plates.

Options

A. `0^(@)`C
B. `2.5^(@)`C
C. `5^(@)`C
D. `6.5^(@)`C

Answer

C

Explanation

c) If T is the temperature of the interface of two plates of same area, then
`(dQ)/(dt) = (K_(1)A(10-7))/(Deltax_(1))=(K_(2)A(T-0))/(Deltax_(2))`
`(K_(1)A(10-T))/(Deltax_(1))=(3/2K_(1)A(T-0))/(3//2Deltax_(1))[thereforeK_(1)/K_(2)=2/3and (Deltax_(1))/(Deltax_(2))=2/3]`
or `10-T=T-0` or T+T = 10 or 2T = 10
`therefore` T = `5^(@)`C