Answer :
Final answer:
To find the final temperature of the water, calculate the heat lost by the aluminum and the heat gained by the water. Equalize both equations since the heat lost by the aluminum equals the heat gained by the water, then solve for the final temperature.
Explanation:
In this problem, the calculation of the final temperature of the water involves finding out how much heat is transferred from the hotter aluminum to the cooler water until both reach an equilibrium temperature. This invokes the principle of heat transfer where heat flows from the hotter object to the cooler object until both are at the same temperature.
First, calculate how much heat is lost by the aluminum using its specific heat, change in temperature, and mass: q = mcΔT, where m is the mass, c is the specific heat, and ΔT is the change in temperature. Since we know the mass of aluminum, its specific heat, and initial temperature, we can write the equation as: q = (2.65E1 g)*(0.903 J/g°C)*(1.005E2°C - [tex]T_f_i_n_a_l[/tex]), where[tex]T_f_i_n_a_l[/tex] is the final temperature.
Simultaneously, the water will gain heat that was lost by the aluminum. Hence, its heat gain can similarly be calculated as q = mcΔT where m is the mass, c is the specific heat, and ΔT is the change in temperature. Substituting values for water, we get the equation: q = (1.005E2 g)*(4.184 J/g°C)*([tex]T_f_i_n_a_l[/tex] - 2.18E1°C).
Since heat lost by aluminum is equal to heat gained by water, we can set the two equations equal to each other and solve for [tex]T_f_i_n_a_l[/tex]. This approach allows us to calculate the final temperature after the heat exchange between the aluminum and water.
Learn more about Heat Transfer in Calorimetry here:
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