A copper block of mass 2.5 kg is heated in a furnace to temperatures of 500° c and thenplaced on a large block of ice. What is the maximum amount of ice that melts? (Specificheat of copper =0.39Jg⁻¹K⁻¹;heat of fusion of water =335Jg⁻¹)
Question
A copper block of mass 2.5 kg is heated in a furnace to temperatures of 500° c and thenplaced on a large block of ice. What is the maximum amount of ice that melts? (Specificheat of copper =0.39Jg⁻¹K⁻¹;heat of fusion of water =335Jg⁻¹)
Solution
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the copper block will be equal to the heat gained by the ice to melt it.
Step 1: Convert the mass of the copper block from kg to g. 1 kg = 1000 g, so 2.5 kg = 2500 g.
Step 2: Convert the temperature change from Celsius to Kelvin. The temperature change is the same in both scales, so the change is 500 K.
Step 3: Calculate the heat lost by the copper block using the formula Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the temperature change. Q = (2500 g)(0.39 J/gK)(500 K) = 487500 J.
Step 4: Calculate the mass of ice melted using the formula Q = mLf, where Q is the heat, m is the mass, and Lf is the heat of fusion. 487500 J = m(335 J/g), so m = 487500 J / 335 J/g = 1455 g.
Therefore, the maximum amount of ice that can be melted by the copper block is 1455 g.
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