Thermal Properties of Matter

JEE Main level, single correct, medium

65 of 126

Question 65 of 126

A copper block of mass 5.0kg5.0kg is heated to a temperature of 500∘C500^{\circ}C and is placed on a large ice block. What is the maximum amount of ice that can melt?
[Specific heat of copper : 0.39Jg−1C∘−10.39{Jg}^{-1}{C^{\circ}}^{-1} and latent heat of fusion of water : 335Jg−1335{Jg}^{-1}]

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Answer: (C) 2.9kg2.9kg

Given, mass of copper block m=5kgm=5kg

Change in temperature (Δt)=500∘C\left(\Delta \text{t}\right)=500^{\circ}\text{C}

Specific heat s=0.39J(g−∘C)−1s=0.39J{(g-^{\circ}C)}^{-1}

Latent heat of fusion of water L=335Jg−1L=335J{g}^{-1}

Heat energy absorbed by copper block, Q1=msΔt{\text{Q}}_{1}=\text{ms}\Delta \text{t}

Let m′m' kgkgof ice be melted.

Heat energy required to melt ice, Q2=m′L{Q}_{2}=m'L

But heat energy absorbed by copper block is heat energy utilised by ice in melting,Q1=Q2{Q}_{1}={Q}_{2}.
msΔt=m′L\text{ms}\Delta \text{t}={\text{m}}^{'}\text{L}
or m′=msΔtL{\text{m}}^{'}=\dfrac{\text{ms} \Delta \text{t}}{\text{L}} =5×0.39×500335=2.9kg=\dfrac{5\times 0.39\times 500}{335}=2.9kg

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