Question

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]

• A. 1.5 kg
• B. 5.8 kg
• C. 2.9 kg
• D. 3.8 kg

Answer 1

The Correct Option is A

To find the maximum amount of ice that can melt when the copper block is placed on it, we need to consider the heat transfer from the copper block to the ice. The copper block will lose heat, which will be absorbed by the ice to undergo a phase change from solid to liquid.

The formula to calculate the heat lost by the copper block is given by:

Q = m \cdot c \cdot \Delta T

where:

• m = 5000 \text{ g} (mass of copper block in grams)
• c = 0.39 \text{ J g}^{-1} \text{°C}^{-1} (specific heat capacity of copper)
• \Delta T = 500 \text{°C} - 0 \text{°C} = 500 \text{°C} (temperature change)

Substituting the values, we get:

Q = 5000 \cdot 0.39 \cdot 500 = 975000 \text{ J}

The heat required to melt ice is calculated using the formula:

Q = m_{\text{ice}} \cdot L_f

where:

• m_{\text{ice}} is the mass of ice melted.
• L_f = 335 \text{ J g}^{-1} (latent heat of fusion of ice)

Equating the heat lost by copper to the heat gained by the ice for melting:

975000 = m_{\text{ice}} \cdot 335

Solving for m_{\text{ice}}:

m_{\text{ice}} = \frac{975000}{335} \approx 2910 \text{ g} = 2.91 \text{ kg}

Correcting for rounding to match any potential options provided, the closest option to this calculation is 2.9 kg. Therefore, the answer should be 2.9 kg.

Note: Make sure the options in the original prompt are checked correctly. If "1.5 kg" is given as the right answer incorrectly, review the problem setup, unit conversions, and accounting procedures.