A 1 kg block of ice at 0°C is placed in 2 kg of water at 20°C. What will be the
Practice Questions
Q1
A 1 kg block of ice at 0°C is placed in 2 kg of water at 20°C. What will be the final temperature of the mixture? (Specific heat of water = 4.2 kJ/kg°C, Latent heat of fusion of ice = 334 kJ/kg) (2021)
0°C
10°C
20°C
15°C
Questions & Step-by-Step Solutions
A 1 kg block of ice at 0°C is placed in 2 kg of water at 20°C. What will be the final temperature of the mixture? (Specific heat of water = 4.2 kJ/kg°C, Latent heat of fusion of ice = 334 kJ/kg) (2021)
Step 1: Identify the masses and temperatures of the ice and water. The ice has a mass of 1 kg and is at 0°C. The water has a mass of 2 kg and is at 20°C.
Step 2: Understand that when the ice is added to the water, the ice will absorb heat to melt and then warm up, while the water will lose heat.
Step 3: Calculate the heat required to melt the ice. Use the formula: Heat = mass × latent heat of fusion. For 1 kg of ice, it will be 1 kg × 334 kJ/kg = 334 kJ.
Step 4: Calculate the heat lost by the water as it cools down. Use the formula: Heat = mass × specific heat × change in temperature. The water will cool down from 20°C to the final temperature (Tf).
Step 5: Set up the equation: Heat lost by water = Heat gained by ice. This means: 2 kg × 4.2 kJ/kg°C × (20°C - Tf) = 334 kJ.
Step 6: Solve the equation for Tf (final temperature). Rearrange the equation to find Tf.
Step 7: Calculate the final temperature using the values from the previous steps.
Heat Transfer – The principle of conservation of energy where heat lost by the warmer substance (water) equals heat gained by the colder substance (ice).
Latent Heat – The energy required to change the state of a substance without changing its temperature, specifically the melting of ice in this case.
Specific Heat Capacity – The amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius, relevant for the water in the problem.
