Same quantity of ice is filled in each of the two metal containers P and having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in P melts completely in time `t_1`, whereas that in Q takes a time `t_2`. The ratio of thermal conductivities of the materials of P and Q is

Options

A. `t_2 : t_1`
B. `t_1:t_2`
C. `t_1 :t_(2)^(2)`
D. `t_(2)^(2) :t_(1)^(2)`

Answer

A

Explanation

Let `K_1 and K_2 ` be the thermal condictivities of containers P and Q respectively
As the same quanitity of ice melts in P and Q the quanitity of heat flows in P and Q must be same
` therefore Q = ( K_1 A(T_1 -T_2 )t_1)/(x) = (K_2 A(T_1 -T_2)t_2)/(x)`
` or K_1 T_1 = k_2 t_2 or (k_1)/(k_2) = (t_2)/(t_1)`