Goal Solve a calorimetry problem involving three substances at three different t

Question

Goal Solve a calorimetry problem involving three substances at three different temperatures.

Problem Suppose 0.400 kg of water initially at 40.0

Goal Solve a calorimetry problem involving three substances at three different temperatures. Problem Suppose 0.400 kg of water initially at 40.0 degree C is poured into a 0.300-kg glass beaker having a temperature of 25.0 degree C. A 0.500-kg block of aluminum at 37.0 degree C is placed in the water and the system insulated. Calculate the final equilibrium temperature of the system. Strategy The energy transfer for the water, aluminum, and glass will be designated Qw, Qal, and Qg, respectively. The sum of these transfers must equal zero, by conservation of energy. Construct a table, assemble the three terms from the given data, and solve for the final equilibrium temperature, T. Apply the final temperature equation to the system. (1) Qw + Qal + Qg = 0 (2) mwcw(T -Tw) + malcal(T -Tal) + mgcg(T -Tg) = 0 Construct a data table. Using the table, substitute into Equation (2). 1. Use the worked example above to help you solve this problem. Suppose 0.390 kg of water initially at 36.0 degree C is poured into a 0.300 kg glass beaker having a temperature of 25.0 degree C. A 0.500 kg block of aluminum at 37.0 degree C is placed in the water, and the system insulated. Calculate the final equilibrium temperature of the system. ________ degree C? 2. A 16.0 kg gold bar at 26.0 degree C is placed in a large, insulated 0.800 kg glass container at 15.0 degree C with 2.00 kg of water at 25.0 degree C. Calculate the final equilibrium temperature. _________ degree C

Explanation / Answer

Using the same principle,

(4190 J/kg C)(0.390 kg)(T - 36 C) + (837 J/kg C)(0.300 kg)(T - 25 C) + (900 J/kg C)(0.500 kg)(T - 37 C) = 0

Thus,

T = 35.0 degrees C   [ANSWER, PART 1]

******************

For gold, c = 1290 J/kg C. Thus,

(4190 J/kg C)(2.00 kg)(T - 25 C) + (837 J/kg C)(0.800 kg)(T - 15 C) + (1290 J/kg C)(16.0 kg)(T - 26 C) = 0

Thus,

T = 24.8 degrees C   [ANSWER, PART 2]

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