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Answer :
To determine the specific heat of the metal, use the conservation of energy principle, equating the heat lost by the metal to the heat gained by the water, and solve for the specific heat of the metal using the known masses and temperatures.
The specific heat of the metal can be calculated using the principle of conservation of energy, which states that the heat lost by the metal must equal the heat gained by the water. We can express this principle through the formula:
- Qmetal = -Qwater
Where Q is the heat transferred, given by the product of mass (m), specific heat capacity (c), and the change in temperature (ΔT). Thus, the calculation is:
- mmetalcmetalΔTmetal = -mwatercwaterΔTwater
Plugging in the known values and solving for cmetal:
- (0.0591 kg)(cmetal)(25.4 °C - 197 °C) = -(0.386 kg)(4186 J/kg°C)(25.4 °C - 23 °C)
Now we can solve for cmetal:
- cmetal = (0.386 kg * 4186 J/kg°C * 2.4 °C) / (0.0591 kg * -171.6 °C)
After calculating, we find the specific heat of the metal.
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