Two identical vessels are filled with equal amount of ice. The vessels are made from different materials. If the ice melts in the two vessels in times $t_{1}$ and $t_{2}$ respectively then their thermal conductivities are in the ratio:

t_{2} : t_{1}

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

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t_{1} : t_{2}

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

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Solution

The correct option is A $t_{2} : t_{1}$
Here, both vessels are identical which implies that both have same cross-sectional areas and length.
Now, $Q = \frac{K A Δ T t}{L}$ and $Q = M L$ , hold for both vessel.
Now, equating heat dissipated by both vessels $Q_{1} = Q_{2}$
So, $\frac{K_{1} A (Δ T) t_{1}}{L} = \frac{K_{2} A (Δ T) t_{2}}{L}$
$\frac{K_{1}}{K_{2}} = \frac{t_{2}}{t_{1}}$

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Two identical vessels are filled with equal amount of ice. The vessels are made from different materials. If the ice melts in the two vessels in times t1 and t2 respectively then their thermal conductivities are in the ratio:

The correct option is A t2:t1Here, both vessels are identical which implies that both have same cross-sectional areas and length.Now, Q=KAΔTtL and Q=ML, hold for both vessel.Now, equating heat dissipated by both vessels Q1=Q2So, K1A(ΔT)t1L=K2A(ΔT)t2LK1K2=t2t1

Two identical vessels are filled with equal amount of ice. The vessels are made from different materials. If the ice melts in the two vessels in times $t_{1}$ and $t_{2}$ respectively then their thermal conductivities are in the ratio: