A piece of Aluminum of mass 3.90 g at temperature 99.3^oC is immersed into a 10.0 cm³ of water at 22.6 ^oC (figure 7.2). Determine the final temperature of the system.

The strings: S₇P₅A₅₁ (Change - Physical).

The math:
Pj Problem of Interest is of type Change (physical).



Assumption: system is insulated
Let q = heat gained or lost; m = mass in grams; C_p = specific heat;
ΔT = change in temperature = T_final - T_initial (when heat is gained).
ΔT = change in temperature = T_initial - T_final (when heat is lost).
By the law of conservation of energy:
q = m(ΔT)C_p --------(1)
q_lost = q_gained -------(2)

Now mass of water = Density x Volume = 1 x 10 g/cm₃.
So from equation (2):
(3.90)(99.3 - T_final)(0.903) = (10)(22.6 - T_final)(4.18)
So, final temperature of system, T_final = 28.6^oC.

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