A copper block of mass 2.5kg is heated in a furnace to a temperat… - Vidyadip

Question

A copper block of mass $2.5kg$ is heated in a furnace to a temperature of $500°C$ and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = $0.39 J g^{–1} K^{–1\}$; heat of fusion of water = $335 J g^{–1}$ ).

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Answer

Mass of the copper block, m = 3kg = 3000g Rise in the temperature of the copper block, $\triangle\theta=500^\circ\text{C}$ Specific heat of copper, $\mathrm{C}=0.39 \mathrm{Jg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ The maximum heat the copper block can lose, $\text{Q}=\text{mc}\triangle\theta=3000\times0.39\times500=5.85\times10^5\text{J}$ Let, $m_1$ be the total amount of ice melted by the hot block of copper. Heat gained by molten ice, $Q = m_1L \therefore\text{m}_1=\frac{\text{Q}}{\text{L}}=\frac{585000}{335}=1746.26\text{g}$

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