A 5 kg block of ice at 0°C is placed in a calorimeter containing 2 kg of water a
Practice Questions
Q1
A 5 kg block of ice at 0°C is placed in a calorimeter containing 2 kg of water at 80°C. What is the final temperature of the system when thermal equilibrium is reached? (Latent heat of fusion of ice = 334 kJ/kg)
0°C
20°C
40°C
60°C
Questions & Step-by-Step Solutions
A 5 kg block of ice at 0°C is placed in a calorimeter containing 2 kg of water at 80°C. What is the final temperature of the system when thermal equilibrium is reached? (Latent heat of fusion of ice = 334 kJ/kg)
Correct Answer: 0°C
Step 1: Identify the mass of the ice block, which is 5 kg, and its initial temperature, which is 0°C.
Step 2: Identify the mass of the water, which is 2 kg, and its initial temperature, which is 80°C.
Step 3: Understand that when the ice is placed in the water, the water will lose heat and the ice will gain heat until they reach the same final temperature.
Step 4: Calculate the heat required to melt the ice using the formula: Heat = mass of ice × latent heat of fusion. Here, it is 5 kg × 334 kJ/kg = 1670 kJ.
Step 5: Calculate the heat lost by the water as it cools down. The water will cool down to the final temperature (Tf). The formula for heat lost is: Heat = mass of water × specific heat of water × change in temperature. The specific heat of water is approximately 4.18 kJ/kg°C.
Step 6: Set up the equation: Heat lost by water = Heat gained by ice. This means: (2 kg × 4.18 kJ/kg°C × (80°C - Tf)) = 1670 kJ.
Step 7: Solve the equation for Tf. After calculations, you will find that Tf equals 0°C.
Step 8: Conclude that the final temperature of the system when thermal equilibrium is reached is 0°C.
Heat Transfer – Understanding how heat is exchanged between substances at different temperatures until thermal equilibrium is reached.
Latent Heat of Fusion – The energy required to change a substance from solid to liquid at its melting point without changing its temperature.
Thermal Equilibrium – The state in which two or more bodies in thermal contact no longer exchange heat, resulting in a uniform temperature.
