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A 200 g piece of metal at 100°C is placed in 300 g of water at 20°C. What is the

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Question: A 200 g piece of metal at 100°C is placed in 300 g of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.18 J/g°C, specific heat of metal = 0.9 J/g°C) (2022)

Options:

  1. 22.5°C
  2. 30°C
  3. 35°C
  4. 40°C

Correct Answer: 35°C

Exam Year: 2022

Solution: 

Using the principle of conservation of energy: m1c1(T_initial - T_final) = m2c2(T_final - T_initial). Solving gives T_final = 35°C.

A 200 g piece of metal at 100°C is placed in 300 g of water at 20°C. What is the

Practice Questions

Q1
A 200 g piece of metal at 100°C is placed in 300 g of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.18 J/g°C, specific heat of metal = 0.9 J/g°C) (2022)
  1. 22.5°C
  2. 30°C
  3. 35°C
  4. 40°C

Questions & Step-by-Step Solutions

A 200 g piece of metal at 100°C is placed in 300 g of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.18 J/g°C, specific heat of metal = 0.9 J/g°C) (2022)
  • Step 1: Identify the masses and specific heats of the substances involved. The mass of the metal (m1) is 200 g, its specific heat (c1) is 0.9 J/g°C. The mass of the water (m2) is 300 g, and its specific heat (c2) is 4.18 J/g°C.
  • Step 2: Write down the initial temperatures. The initial temperature of the metal (T_initial_metal) is 100°C, and the initial temperature of the water (T_initial_water) is 20°C.
  • Step 3: Set up the equation based on the principle of conservation of energy. The heat lost by the metal will equal the heat gained by the water: m1 * c1 * (T_initial_metal - T_final) = m2 * c2 * (T_final - T_initial_water).
  • Step 4: Substitute the known values into the equation: 200 g * 0.9 J/g°C * (100°C - T_final) = 300 g * 4.18 J/g°C * (T_final - 20°C).
  • Step 5: Simplify the equation: 180 * (100 - T_final) = 1254 * (T_final - 20).
  • Step 6: Distribute and rearrange the equation to isolate T_final: 18000 - 180 * T_final = 1254 * T_final - 25080.
  • Step 7: Combine like terms: 18000 + 25080 = 180 * T_final + 1254 * T_final.
  • Step 8: Solve for T_final: 43080 = 1434 * T_final, so T_final = 43080 / 1434.
  • Step 9: Calculate T_final to find the final temperature: T_final ≈ 30°C.
  • Heat Transfer – The question tests the understanding of heat transfer between two substances and the principle of conservation of energy.
  • Specific Heat Capacity – It assesses the ability to apply the specific heat formula to calculate the final temperature of a system.
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