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A copper block of mass 5.0 kg is heated to a temperature of 500 °C and is 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 ° C⁻¹ and latent heat of fusion of water =335 J g⁻¹)

Asked in JEE Main 25th June 2nd Shift 2022 · Latent heat and change of state

• (1) 1.5 kg
• (2) 5.8 kg
• (3) 2.9 kg
• (4) 3.8 kg

Step-by-step solution

Why the other options are wrong

• (1) comes from is about half the key, the size you get by halving the copper's temperature drop; the block cools all the way to 0 °C because the ice block is large, so the full 500 °C is available.
• (2) comes from is the key doubled; it is what a 10 kg block, or a drop of 1000 °C, would melt. As a check, each gram of copper cooling 500 °C can melt only (0.39×500)/(335)=0.58 g of ice, so 5000 g melts 2910 g.
• (4) comes from no consistent slip lands here; it is a filler above the key. The obvious wrong route, forgetting that the copper's mass is 5000 g and not 5 g, changes the answer by a factor of 1000, not by 30%.

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