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

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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 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) (2021)

Options:

  1. 25°C
  2. 30°C
  3. 35°C
  4. 40°C

Correct Answer: 35°C

Exam Year: 2021

Solution: 

Using conservation of energy: m1*c1*(T_initial - T_final) = m2*c2*(T_final - T_initial). Solving gives T_final = 35°C.

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

Practice Questions

Q1
A 1 kg block of metal at 100°C is placed in 2 kg 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) (2021)
  1. 25°C
  2. 30°C
  3. 35°C
  4. 40°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 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) (2021)
  • Step 1: Identify the masses and specific heats of the materials involved. The mass of the metal block (m1) is 1 kg, and its specific heat (c1) is 0.9 J/g°C. The mass of the water (m2) is 2 kg, and its specific heat (c2) is 4.18 J/g°C.
  • Step 2: Convert the masses from kg to grams because the specific heats are given in J/g°C. So, m1 = 1000 g (1 kg) and m2 = 2000 g (2 kg).
  • Step 3: 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 4: Set up the equation using 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 5: Substitute the known values into the equation: 1000 g * 0.9 J/g°C * (100°C - T_final) = 2000 g * 4.18 J/g°C * (T_final - 20°C).
  • Step 6: Simplify the equation: 900 * (100 - T_final) = 8360 * (T_final - 20).
  • Step 7: Distribute and rearrange the equation to isolate T_final: 90000 - 900*T_final = 8360*T_final - 167200.
  • Step 8: Combine like terms: 90000 + 167200 = 8360*T_final + 900*T_final.
  • Step 9: Solve for T_final: 257200 = 9260*T_final, so T_final = 257200 / 9260.
  • Step 10: Calculate T_final to find the final temperature of the system, which is approximately 35°C.
  • Heat Transfer – The principle of conservation of energy applied to heat transfer between two substances.
  • Specific Heat Capacity – Understanding how different materials absorb and transfer heat based on their specific heat values.
  • Equilibrium Temperature – Determining the final temperature when two substances at different temperatures reach thermal equilibrium.
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