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 $t_{1}$ whereas that in Q takes a time $t_{2}$ . The ratio of thermal conductivities of the materials of P and Q is

t_{2} : t_{1}

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t_{1} : t_{2}

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t_{1}^{2} : t_{2}^{2}

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t_{2}^{2} : t_{1}^{2}

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Solution

The correct option is A $t_{2} : t_{1}$
The power transported per unit area is given as
$\frac{Δ Q}{A Δ t} = - κ \frac{Δ T}{Δ x}$
Thus $Δ Q = - κ Δ t A \frac{Δ T}{Δ x}$
Same amount of heat was needed to melt ice in both P and Q. Hence
$κ_{P} t_{1} = κ_{Q} t_{2}$
$⟹ \frac{κ_{P}}{κ_{Q}} = \frac{t_{2}}{t_{1}}$

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The correct option is A t2:t1The power transported per unit area is given asΔQAΔt=−κΔTΔxThus ΔQ=−κΔtAΔTΔxSame amount of heat was needed to melt ice in both P and Q. Hence κPt1=κQt2⟹κPκQ=t2t1