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A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be

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Question: A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be the final temperature of the system assuming no heat loss? (2022)

Options:

  1. 30°C
  2. 40°C
  3. 50°C
  4. 60°C

Correct Answer: 50°C

Exam Year: 2022

Solution: 

Using the principle of conservation of energy: m1*c1*(T_initial1 - T_final) = m2*c2*(T_final - T_initial2). Solving gives T_final = 50°C.

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be

Practice Questions

Q1
A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be the final temperature of the system assuming no heat loss? (2022)
  1. 30°C
  2. 40°C
  3. 50°C
  4. 60°C

Questions & Step-by-Step Solutions

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What will be the final temperature of the system assuming no heat loss? (2022)
  • Step 1: Identify the masses and initial temperatures of the two objects. The metal block has a mass (m1) of 1 kg and an initial temperature (T_initial1) of 100°C. The water has a mass (m2) of 2 kg and an initial temperature (T_initial2) of 20°C.
  • Step 2: Write down the specific heat capacities. For simplicity, we can use c1 for the metal and c2 for water. The specific heat capacity of water is typically 4.18 J/g°C, but we will keep it as c2 for now.
  • Step 3: Use the conservation of energy principle. This means that the heat lost by the metal block will equal the heat gained by the water. We can express this as: m1 * c1 * (T_initial1 - T_final) = m2 * c2 * (T_final - T_initial2).
  • Step 4: Substitute the known values into the equation. We have: 1 kg * c1 * (100°C - T_final) = 2 kg * c2 * (T_final - 20°C).
  • Step 5: Rearrange the equation to solve for T_final. This involves isolating T_final on one side of the equation.
  • Step 6: Solve the equation. After performing the calculations, we find that T_final = 50°C.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transferred or converted from one form to another, applied here to heat transfer between the metal block and water.
  • Specific Heat Capacity – The amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius, which is crucial for calculating temperature changes in different materials.
  • Heat Transfer – The process of thermal energy moving from the hotter object (metal) to the cooler object (water) until thermal equilibrium is reached.
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