The coefficient of thermal conductivity of copper, mercury and glass are respectively `K_(c), K_(m)` and `K_(g)` that `K_(c) gt K_(m) gt K_(g)`. If the same quantity of heat is to flow per second per unit of each and corresponding temperature gradients are `X_(c), X_(m)` and `X_(g)`, then

Options

A. `X_(c) = X_(m) = X_(g)`
B. `X_(c) lt X_(m) gt X_(g)`
C. `X_(c) lt X_(m) lt X_(g)`
D. `X_(m) lt X_(c) lt X_(g)`

Answer

C

Explanation

`(Q)/(At) = K (Delta theta)/(l) rArr K(Delta theta)/(l) =` consta nt
`rArr (Delta theta)/(l) prop (l)/(K)`
Hence, if `K_(c) gt K_(m) gt K_(g)`, then
`((Delta theta)/(l))_(c) lt ((Delta theta)/(l))_(m) lt ((Delta theta)/(l))_(g) rArr X_(c) lt X_(m) lt X_(g)`
Because higher `K` implies lower value of the temerature gradient.