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? (Assume no heat loss to the surroundings)
0°C
10°C
15°C
20°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? (Assume no heat loss to the surroundings)
Step 1: Identify the masses and temperatures of the ice and water. The mass of ice is 1 kg at 0°C, and the mass of water is 2 kg at 20°C.
Step 2: Understand that the heat lost by the water will equal the heat gained by the ice. This is based on the principle of conservation of energy.
Step 3: Calculate the heat lost by the water as it cools down to the final temperature (Tf). The formula is Q = mcΔT, where m is mass, c is specific heat capacity (for water, it's 4.18 J/g°C), and ΔT is the change in temperature.
Step 4: Calculate the heat gained by the ice as it melts and then warms up to the final temperature. The heat gained by the ice includes the heat to melt it (Q = mL, where L is the latent heat of fusion) and the heat to warm the melted ice (Q = mcΔT).
Step 5: Set the heat lost by the water equal to the heat gained by the ice and solve for the final temperature (Tf).
Step 6: After calculations, find that the final temperature of the mixture is approximately 10°C.
Conservation of Energy – The principle that the total energy in a closed system remains constant, meaning the heat lost by the warmer substance (water) equals the heat gained by the colder substance (ice).
Phase Change – Understanding that ice at 0°C will absorb heat to melt before its temperature can increase, which is crucial for calculating the final temperature.
Heat Transfer Calculations – Applying the formula Q = mcΔT to calculate the heat transfer for both the water and the ice.
