To find the specific heat of aluminum, we can use the principle of conservation of energy. The heat lost by the aluminum will be equal to the heat gained by the water. The formula for calculating heat transfer is:
Q = m * c * ΔT
Where: Q is the heat transferred m is the mass of the substance c is the specific heat capacity of the substance ΔT is the change in temperature
In this case, the heat lost by the aluminum is equal to the heat gained by the water:
Q_aluminum = Q_water
m_aluminum * c_aluminum * ΔT_aluminum = m_water * c_water * ΔT_water
Given: m_aluminum = 100 g c_water = 4.18 J/g°C (specific heat of water) ΔT_aluminum = 100°C - 25°C = 75°C m_water = 100 g ΔT_water = 25°C - 10°C = 15°C
Plugging in the values, we get:
100 g * c_aluminum * 75°C = 100 g * 4.18 J/g°C * 15°C
Simplifying the equation:
c_aluminum = (100 g * 4.18 J/g°C * 15°C) / (100 g * 75°C)
c_aluminum = 0.557 J/g°C
Therefore, the specific heat of aluminum is approximately 0.557 J/g°C.