200 grams of water is in a 60 gram aluminum cup (part of a well insulated calori

Question

200 grams of water is in a 60 gram aluminum cup (part of a well insulated calorimeter). A thermometer of negligible mass is immersed in the water and has read 22 ?C for the last 20 minutes. A 50 gram copper cylinder that has been in a freezer (interior temperature of -8?C) all night is quickly removed from the freezer and dropped into the water.  Assuming that the system consisting of the water, the cup and the cylinder is closed to energy flows: a)What does the thermometer read after the cylinder has been in the water for a long time? b) If the cup (still containing the water and the copper cylinder) is removed from the calorimeter and allowed to warm to the room temperature (also 22?C) how much energy flows into the system?

Explanation / Answer

specific heat of aluminium = 0.91 Kj/kg

specific heat of copper = 0.39 Kj/kg

specific heat of water = 4.186 Kj/kg

let equilibrium temperature be t

heat lost by water + calorimeter = heat gained by the copper cylinder

((0.2*4.186)+ (0.06*0.91))*(22-t) = 0.05*0.39*(t+8)

0.8918*(22-t)=0.0195(t+8)

19.6196 - 0.8918t = 0.0195t + 0.156

19.4636 = 0.9113 *t

t=21.358 celsius is the temperature read by the thermometer

the energy flows into the system till the temperature becomes 22 celsius

therefore

energy flownto the system

((0.2*4.186)+ (0.06*0.91)+(0.05*0.39))*(22-21.358)

=0.5850546 joules

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