# Same quantity of ice is filled in each of the two metal container P and Q having the same size, shape and will thickness but make of different materia

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Same quantity of ice is filled in each of the two metal container P and Q having the same size, shape and will thickness but make of different materials. The containers are kept in identical surroundings, The ice in P melts completely in time t_(1), whereas in Q takes a time t_(2). The ratio of thermal conductivities of hte materials of P and Q is:
A. t_(2):t_(1)
B. t_(1):t_(2)
C. t_(1)^(2):t_(2)^(2)
D. t_(2)^(2):t_(1)^(2)

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a) We know that, relation between the temperature gradient (TG) and thermal conductivity (K),
(dQ)/(dt) = -KA(d(theta))/(dx)=-KAxx(TG)
i.e., TG alpha 1/K (dQ)/(dt) = constant
or Kalpha1/t rArrK_(1)alpha1/(t_(1))...........(i)
K_(2)alpha1/t_(2)..............(ii)
From the Eqs. (i) and (ii), we get
K_(1)/K_(2)=(1//t_(1))/(1//t_(2)) rArrK_(1):K_(2)=t_(2):t_(1)