In a physics lab students are conducting an experiment to learn about the heat c

Question

In a physics lab students are conducting an experiment to learn about the heat capacity of different materials. The first group is instructed to add 1.5-g copper pellets at a temperature of 92°C to 295 g of water at 16°C. A second group is given the same number of 1.5-g pellets as the first group, but these are now aluminum pellets. Assume that no heat is lost to or gained from the surroundings for either group.

(a) If the final equilibrium temperature of the copper pellets and water is 27°C, how many whole pellets did the first group use in the experiment? The specific heat of copper is 0.0924 kcal/(kg · °C).
pellets

(b) Will the final equilibrium temperature for the second group be higher, lower, or the same as for the first group? The specific heat of aluminum is 0.215 kcal/(kg · °C).

higherlower    the same

(c) What is the equilibrium temperature of the aluminum and water mixture for the second group?

Explanation / Answer

a)

n = number of copper pellets

mcu = mass of each copper pellets = 1.5 x 10-3 kg

mw = mass of water = 295 g = 0.295 kg

cw = specific heat of water = 1000  

ccu = specific heat of copper = 92.4

using conservation of heat

Heat lost by copper pallets = heat gained by water

n mcu ccu (92 - 27) = mw cw (27 - 16)

n (1.5 x 10-3) (92.4) (92 - 27) = (0.295) (1000) (27 - 16)

n = 360

b)

n = number of copper pellets = 360

mal = mass of each aluminium pellets = 1.5 x 10-3 kg

mw = mass of water = 295 g = 0.295 kg

cw = specific heat of water = 1000  

cal = specific heat of aluminium = 215

using conservation of heat

Heat lost by aluminium pallets = heat gained by water

n mal cal (92 - 27) = mw cw (T - 16)

(360) (1.5 x 10-3) (215) (92 - T) = (0.295) (1000) (T - 16)

T = 37.5

higher

c)

T = 37.5

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