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)
Practice Questions
1 question
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
Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. Final temperature can be calculated to be approximately 10°C.
Questions & Step-by-step Solutions
1 item
Q
Q: 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)
Solution: Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. Final temperature can be calculated to be approximately 10°C.
Steps: 6
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.
