To find the resulting temperature when the hot iron is dropped into the water, we need to consider the heat lost by the iron, the heat gained by the water, and the heat gained by the iron vessel.
The heat lost by the iron when it cools down can be calculated using the formula:
Q_iron = m_iron * c_iron * (Tf - Ti)
Where:
m_iron = 80 g (mass of iron)
c_iron = 0.449 J/g°C (specific heat capacity of iron)
Tf = Resulting temperature
Ti = Initial temperature = 100°C
The heat gained by the water can be calculated using the formula:
Q_water = m_water * c_water * (Tf - Ti)
Where:
m_water = 200 g (mass of water)
c_water = 4.18 J/g°C (specific heat capacity of water)
Ti = Initial temperature = 20°C
The heat gained by the iron vessel can be calculated using the formula:
Q_vessel = m_vessel * c_vessel * (Tf - Ti)
Where:
m_vessel = 50 g (mass of iron vessel)
c_vessel = 0.449 J/g°C (specific heat capacity of iron)
Ti = Initial temperature = 20°C
Since the total heat lost by the iron is equal to the total heat gained by the water and the iron vessel, we can set up the equation:
Q_iron = Q_water + Q_vessel
Plugging in the values and solving the equation will give us the resulting temperature (Tf).