A 2 kg block of metal at 100°C is placed in 1 kg of water at 20°C. What is the f
Practice Questions
Q1
A 2 kg block of metal at 100°C is placed in 1 kg of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.2 J/g°C, specific heat of metal = 0.9 J/g°C) (2021)
30°C
40°C
50°C
60°C
Questions & Step-by-Step Solutions
A 2 kg block of metal at 100°C is placed in 1 kg of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.2 J/g°C, specific heat of metal = 0.9 J/g°C) (2021)
Step 1: Identify the masses and specific heats of the materials involved. The mass of the metal block is 2000 grams (2 kg) and its specific heat is 0.9 J/g°C. The mass of the water is 1000 grams (1 kg) and its specific heat is 4.2 J/g°C.
Step 2: Set up the heat transfer equation. The heat lost by the metal will equal the heat gained by the water. This can be written as: (mass of metal) * (specific heat of metal) * (change in temperature of metal) = (mass of water) * (specific heat of water) * (change in temperature of water).
Step 3: Define the initial and final temperatures. The initial temperature of the metal is 100°C and the initial temperature of the water is 20°C. Let the final temperature be T.
Step 4: Write the equation for heat lost by the metal: 2000 g * 0.9 J/g°C * (100°C - T) = heat lost by metal.
Step 5: Write the equation for heat gained by the water: 1000 g * 4.2 J/g°C * (T - 20°C) = heat gained by water.
Step 6: Set the heat lost by the metal equal to the heat gained by the water: 2000 * 0.9 * (100 - T) = 1000 * 4.2 * (T - 20).
Step 7: Simplify and solve the equation for T. This will involve distributing and combining like terms.
Step 8: After solving the equation, you will find that the final temperature T is 50°C.
Heat Transfer – The principle of conservation of energy where heat lost by the metal equals heat gained by the water.
Specific Heat Capacity – The amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius.
Thermal Equilibrium – The state reached when two substances at different temperatures come into contact and exchange heat until they reach the same temperature.
