Final answer:
After introducing hot aluminum and iron pieces into 97.3 g of water at 22.0°C, the final temperature (\(T_f\)) the water reaches, assuming no heat loss to the surroundings, is approximately 50.7°C.
the correct option is b.
Step-by-step explanation:
The student is asking to calculate the final temperature of water when aluminum and iron, both heated to 100°C, are introduced into it. This is a classic physics problem that involves the concept of heat transfer and the principle of conservation of energy.
When two bodies of different temperatures are brought into contact, heat will flow from the hotter body to the cooler one until thermal equilibrium is reached. The formula for calculating the heat gained or lost by a substance is Q = mc∆T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ∆T is the change in temperature.
To solve this problem, we assume that the heat lost by the hot metals is equal to the heat gained by the water, as there is no heat loss to the surroundings. We can set up the following equation:
(Mass of Al * Specific heat of Al * Change in temperature of Al) + (Mass of Fe * Specific heat of Fe * Change in temperature of Fe) = (Mass of water * Specific heat of water * Change in temperature of water)
After substituting the known values and solving the equation for the final temperature of the water, which is the same as the final temperature for both metals, we should arrive at the correct answer. The specific heat capacity of water is typically taken as 4.18 J/g°C.
the correct option is b.