A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. Assuming no h

Practice Questions

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. Assuming no heat loss to the surroundings, what is the final temperature of the system? (Specific heat of water = 4.18 kJ/kg°C, specific heat of metal = 0.9 kJ/kg°C) (2020)

25°C
30°C
35°C
40°C

Questions & Step-by-Step Solutions

Step 1: Identify the masses and specific heats of the metal and water. The mass of the metal block is 1 kg and its specific heat is 0.9 kJ/kg°C. The mass of the water is 2 kg and its specific heat is 4.18 kJ/kg°C.
Step 2: Set up the equation for heat transfer. 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 final temperature as 'T'. The initial temperature of the metal is 100°C and the initial temperature of the water is 20°C.
Step 4: Write the change in temperature for the metal: (100 - T) and for the water: (T - 20).
Step 5: Substitute the values into the equation: 1 kg * 0.9 kJ/kg°C * (100 - T) = 2 kg * 4.18 kJ/kg°C * (T - 20).
Step 6: Simplify the equation: 0.9 * (100 - T) = 8.36 * (T - 20).
Step 7: Distribute both sides: 90 - 0.9T = 8.36T - 167.2.
Step 8: Combine like terms: 90 + 167.2 = 8.36T + 0.9T.
Step 9: Solve for T: 257.2 = 9.26T, so T = 257.2 / 9.26.
Step 10: Calculate the final temperature T.

Heat Transfer – The principle that heat lost by the hotter object (metal) equals the heat gained by the cooler object (water) in a closed system.
Specific Heat Capacity – The amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius.
Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. Assuming no h

Practice Questions

Questions & Step-by-Step Solutions

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