A 20.00 g chunk of aluminum metal with an initial temperature of 80.0 degree C i

Question

A 20.00 g chunk of aluminum metal with an initial temperature of 80.0 degree C is dropped into a 50.0 g cup of water with an initial temperature of 20.0 degree C. What is the temperature of this system at equilibrium if it is thermally isolated The molar isobaric heat capacity of silver metal obeys the function C_p, m = 26.12 - 0.0110 T/K + 3.826 times 10^-5 T^2/K^2 + 3.750 * 10^-8 T^3/K^3 + 1.396 * 10^-11 T^4/K^4 between the temperatures of 290 and 800 K. C_p, m in this equation is in units of j/mol K. Determine the amount of heat released when a 500. g silver stake pierces the heart of a vampire and cools from 315 to 290 K.

Explanation / Answer

I have a doubt with the number 4, but I can help you with number 3:

Q = m*cp*(Tf - Ti)

Cp for Aluminum = 897 J / g °C

Cp of water = 4180 J / g °C

Aluminium would be 1 and water 2:

Q1 = Q2

20 * 897 (Tf - 80) = 50 * 4180 (20 - Tf)

17940(Tf - 80) = 209000(20-Tf)

17940Tf - 1435200 = 4180000 - 209000Tf

(209000 + 17940)Tf = 4180000 + 1435200

Tf = 56152000 / 226940

Tf = 24.74 °C

Hope this helps

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