Same quantity of ice is filled in each of the two metal containers P and Q 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 $$t1$$, whereas in Q takes a time $$t2$$. The ratio of thermal conductivities of the materials of P and Q is

Question

Infinity Learn · Accepted Answer

We know that, relation between the temperature gradient (TG) and thermal conductivity (K),$$dQdt=$$−KAdθ$$dx=$$−KA×(TG)i$$.e. TG∝$$1K$$    ∵$$dQdt=$$ constant or     K∝$$1t$$⇒       $$K1$$∝$$1t1$$                ... $$(i)and$$     $$K2$$∝$$1t2$$                  ... $$(ii)From$$ Eqs. $$(i) and (ii), we get $$K1K2=1/t11/t2$$⇒ $$K1$$:$$K2=t2$$:$$t1$$

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