The thermal conductivity of brick is `1.7 W m^(-1) K^(-1)`, and that of cement is `2.9 W m^(-1) K^(-1)`.What thickness of cement will have same insulation as the brick of thickness `20 cm`.

Explanation

Since `Q = (KA (T_(1) - T_(2)) t)/(L)`
For same insulation by the brick and cement Q , A `(T_(1) - T_(2))` and t do not change .
That is `, (K)/(L)` should be a constant .
Thus , if `K_(1)` and `K_(2)` be the thermal conductivities of brick and cement and `L_(1)` and `L_(2)` be the required thickness then :
`(K_(1))/(L_(1)) = (K_(2))/(L_(1))` or `(1.7 W^(-1) K^(-1))/(20 cm ) = (2.9 W m^(-1) K^(-1))/(L_(2))`
`therefore L_(2) = (2.9)/(1.7) xx 20 cm = 34.12 ` cm .