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Questions based on phase change

Question

A copper block of mass 2.5 kg is heated in a furnace to a temperature of $500^{0} C$ and then placed on a large ice block. What is the maximum amount (approx.) of ice that can melt? (Specific heat of copper = 0.39 $J / g^{0} C latent heat of fusion of i c e = 335 J / g)$

Moderate

A

2 kg
B

1.5 kg
C

2.5 kg
D

0.5 kg

Solution

Here, mass of copper block,
M = 2.5 kg = 2.5 $\times 10^{3} g$
Rise in temperature of the copper block,
$∆ T = 500^{0} C - 0^{0} C = 500^{0} C$
Specific heat of copper. c = 0.39 $J / g^{0} C$
Latent heat of fusion of water, L = 335 J/g
If m is the mass of ice melted, applying the principle of calorimetry,
Heat gained by ice = heat lost by copper block
i.e., mL = Mc $∆T$
or m = $\frac{Mc ∆ T}{L}$
= $\frac{2.5 \times 10^{3} (g) \times 0.39 (J / {gC}^{0}) \times 500 (C^{o})}{335 (J / g)}$
= 1455 g = 1.455 = 1.5 kg

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