Final answer:
The final equilibrium temperature of a mixture of water and steel is found using the principle of conservation of energy, with the heat lost by the steel equal to the heat gained by the water. The mass and specific heat of both substances, as well as the initial temperatures, are used to set up an equation that can be solved for the final temperature.
Step-by-step explanation:
To find the final equilibrium temperature of a system consisting of water and steel when they are mixed, we can use the principle of conservation of energy. The heat lost by the steel will be gained by the water until thermal equilibrium is reached. The formula for heat transfer is:
Q = mcΔT
where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The equation for the water and steel when they reach equilibrium is:
(mass of steel * specific heat of steel * change in temperature of steel) = (mass of water * specific heat of water * change in temperature of water)
Given that the mass of water is 4150g (4.15 kg), initial temperature is 9.5°C, specific heat is 1 cal/g°C, mass of steel is 410g (0.41 kg), initial temperature is 245°C and specific heat is 0.108 cal/g°C, and assuming no heat loss to the surroundings, we can set up the following equation:
(410g * 0.108 cal/g°C * (Final temperature - 245°C)) = (4150g * 1 cal/g°C * (Final temperature - 9.5°C))
The final temperature can be found by solving for it in the equation above.