Question

Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio `2:3`. The outer surface of one plate is maintained at `10^(@)`C and that of the other at `0^(@)`C. What is the temperature at the common surface?
A. `0^(@)`C
B. `2.5^(@)`C
C. `5^(@)`C
D. `6.5^(@)`C

Answer 1

Correct Answer - C
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