Understanding the Concepts
* Heat Transfer: When objects at different temperatures come into contact, heat flows from the hotter object to the colder object until they reach thermal equilibrium (the same temperature).
* Specific Heat Capacity: The amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius.
Calculations
1. Identify Variables:
* Mass of metal (m₁): 120 grams
* Initial temperature of metal (T₁): 88 °C
* Mass of water (m₂): 250 grams
* Initial temperature of water (T₂): 16 °C
* Final temperature of the mixture (T): 17.5 °C
* Specific heat capacity of water (c₂): 4.184 J/g°C (we'll assume this is the same for the metal, but if you know the metal, you can use its specific heat capacity)
2. Apply the Heat Transfer Equation:
The heat lost by the metal (Q₁) equals the heat gained by the water (Q₂):
Q₁ = Q₂
* Q₁ = m₁ * c₁ * (T₁ - T)
* Q₂ = m₂ * c₂ * (T - T₂)
3. Solve for the Specific Heat Capacity of the Metal (c₁):
Since we know all the other variables except c₁, we can rearrange the equation and solve:
m₁ * c₁ * (T₁ - T) = m₂ * c₂ * (T - T₂)
c₁ = (m₂ * c₂ * (T - T₂)) / (m₁ * (T₁ - T))
c₁ = (250 g * 4.184 J/g°C * (17.5 °C - 16 °C)) / (120 g * (88 °C - 17.5 °C))
c₁ ≈ 0.42 J/g°C
Conclusion
The specific heat capacity of the metal is approximately 0.42 J/g°C.
Important Note: The specific heat capacity of water is a common value, but the specific heat capacity of the metal will vary depending on the type of metal. If you know the metal's identity, you can look up its specific heat capacity and verify the calculations.
