A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature of the system is 30°C, what is the specific heat capacity of the metal? (Specific heat of water = 4.18 J/g°C) (2020)
Practice Questions
1 question
Q1
A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature of the system is 30°C, what is the specific heat capacity of the metal? (Specific heat of water = 4.18 J/g°C) (2020)
0.5 J/g°C
1.0 J/g°C
1.5 J/g°C
2.0 J/g°C
Using the principle of conservation of energy, calculate the specific heat capacity of the metal.
Questions & Step-by-step Solutions
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Q
Q: A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. If the final temperature of the system is 30°C, what is the specific heat capacity of the metal? (Specific heat of water = 4.18 J/g°C) (2020)
Solution: Using the principle of conservation of energy, calculate the specific heat capacity of the metal.
Steps: 10
Step 1: Identify the mass of the metal block (m_metal) and its initial temperature (T_initial_metal). Here, m_metal = 1 kg and T_initial_metal = 100°C.
Step 2: Identify the mass of the water (m_water) and its initial temperature (T_initial_water). Here, m_water = 2 kg and T_initial_water = 20°C.
Step 3: Identify the final temperature of the system (T_final). Here, T_final = 30°C.
Step 4: Convert the masses from kg to grams because the specific heat of water is given in J/g°C. So, m_metal = 1000 g and m_water = 2000 g.
Step 5: Use the formula for heat transfer: Q = mcΔT, where Q is the heat gained or lost, m is mass, c is specific heat capacity, and ΔT is the change in temperature.
Step 6: Calculate the heat lost by the metal: Q_metal = m_metal * c_metal * (T_initial_metal - T_final).
Step 7: Calculate the heat gained by the water: Q_water = m_water * c_water * (T_final - T_initial_water).
Step 8: Set the heat lost by the metal equal to the heat gained by the water: Q_metal = Q_water.
Step 9: Substitute the known values into the equation: 1000 g * c_metal * (100°C - 30°C) = 2000 g * 4.18 J/g°C * (30°C - 20°C).
Step 10: Solve for c_metal (specific heat capacity of the metal).
