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A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final

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Question: A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature is 30°C, what is the specific heat capacity of the metal? (2023)

Options:

  1. 0.5 J/kg°C
  2. 1 J/kg°C
  3. 2 J/kg°C
  4. 4 J/kg°C

Correct Answer: 2 J/kg°C

Exam Year: 2023

Solution: 

Using conservation of energy: m1c1(T1 - Tf) = m2c2(Tf - T2), we find c1 = 2 J/kg°C.

A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final

Practice Questions

Q1
A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature is 30°C, what is the specific heat capacity of the metal? (2023)
  1. 0.5 J/kg°C
  2. 1 J/kg°C
  3. 2 J/kg°C
  4. 4 J/kg°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. If the final temperature is 30°C, what is the specific heat capacity of the metal? (2023)
  • Step 1: Identify the variables. We have a metal block with mass m1 = 1 kg, initial temperature T1 = 100°C, and final temperature Tf = 30°C. We also have water with mass m2 = 2 kg, initial temperature T2 = 20°C, and final temperature Tf = 30°C.
  • Step 2: Write down the formula for conservation of energy. The heat lost by the metal will equal the heat gained by the water: m1 * c1 * (T1 - Tf) = m2 * c2 * (Tf - T2).
  • Step 3: Substitute the known values into the equation. We know m1 = 1 kg, T1 = 100°C, Tf = 30°C, m2 = 2 kg, T2 = 20°C, and we need to find c1 (the specific heat capacity of the metal). The specific heat capacity of water (c2) is approximately 4 J/kg°C.
  • Step 4: Calculate the left side of the equation: 1 kg * c1 * (100°C - 30°C) = 1 kg * c1 * 70°C.
  • Step 5: Calculate the right side of the equation: 2 kg * 4 J/kg°C * (30°C - 20°C) = 2 kg * 4 J/kg°C * 10°C = 80 J.
  • Step 6: Set the two sides of the equation equal to each other: 1 kg * c1 * 70°C = 80 J.
  • Step 7: Solve for c1: c1 = 80 J / (1 kg * 70°C) = 80 / 70 = 1.14 J/kg°C.
  • Step 8: Round the answer to two decimal places if necessary. The specific heat capacity of the metal is approximately 1.14 J/kg°C.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transferred, which is applied here to find the specific heat capacity.
  • Specific Heat Capacity – The amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius.
  • 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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