To determine the temperature change of the skillet, we need to calculate the amount of heat transferred between the water and the skillet. The equation for heat transfer is given by:
Q = m * c * ΔT
Where:
Q = amount of heat transferred (in joules)
m = mass of the substance (in kilograms)
c = specific heat capacity of the substance (in joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
First, let's calculate the amount of heat transferred from the water to the skillet. We'll use the equation:
Q_water = m_water * c_water * ΔT_water
Given:
m_water = 11.2 ml = 0.0112 kg (since 1 ml of water has a mass of approximately 1 g)
c_water = specific heat capacity of water = 4.18 J/(g·°C) = 4180 J/(kg·°C)
ΔT_water = 100°C - 23°C = 77°C
Substituting the values into the equation:
Q_water = 0.0112 kg * 4180 J/(kg·°C) * 77°C
Q_water = 3498.176 J (rounded to four decimal places)
Next, let's calculate the amount of heat absorbed by the skillet:
Q_skillet = m_skillet * c_skillet * ΔT_skillet
Given:
m_skillet = 1.5 kg
c_skillet = 25.19 J/(m·°C)
ΔT_skillet = ?
Since the water is being converted into steam at its boiling point of 100°C, we can assume that the skillet's temperature will also increase to 100°C. Therefore, the change in temperature for the skillet is:
ΔT_skillet = 100°C - Initial Temperature (let's assume the initial temperature is 23°C)
ΔT_skillet = 77°C
Substituting the values into the equation:
Q_skillet = 1.5 kg * 25.19 J/(m·°C) * 77°C
Q_skillet = 2928.885 J (rounded to four decimal places)
Finally, we need to determine the temperature change of the skillet. Since the water transferred heat to the skillet, we can equate the two equations:
Q_water = Q_skillet
3498.176 J = 2928.885 J
Now, let's solve for ΔT_skillet:
ΔT_skillet = Q_skillet / (m_skillet * c_skillet)
ΔT_skillet = 2928.885 J / (1.5 kg * 25.19 J/(m·°C))
ΔT_skillet = 77.413 °C
Therefore, the temperature change of the skillet is approximately 77.4°C.