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Q.

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

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a

t2 : t1

b

t1 : t2

c

t12 : t22

d

t22:t12

answer is A.

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Detailed Solution

We know that, relation between the temperature gradient (TG) and thermal conductivity (K),dQdt=−KAdθdx=−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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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