Suppose that the aluminum cup inside a calorimeter has a mass of 48 g and contai

ID: 2274980 • Letter: S

Question

Suppose that the aluminum cup inside a calorimeter has a mass of 48 g

and contains 84 g of water. Both the cup and water are initially at a

temperature of 5.6 degrees C. You now add an aluminum sample of mass 19.0

g that has been heated in hot water to a temperature of 55.4 degrees C. When

the cup, water, and sample come to equilibrium, their temperature is

7.6 degrees C. Assume that the calorimeter is perfect (i.e., the cup, water, and

sample are thermally isolated from the environment), and that you

know the specific heat of water to be 4190 J/(kg K). On the basis of

these measurements, what is your best estimate of the specific heat of

the aluminum? [You should assume that the aluminum cup and sample

have the same (unknown) value for specific heat.]

energy reqiured for raising the temp of water by 2 degree 4190*84*10^-3*2=703920*10^-3

energy required for raising the temp of alum inium cup=s*48*10^-3*2,s=specific heat capacity of alumiinium

this energy comes at the expense of hot aluminium sample whose temp goes from 55.4 to 7.6 degree

i.e loss in energy=s*19*10^-3*47.8

using conservation of energy we get,703920*10^-3=s((48*10^-3*2)-(19*10^-3*47.8))

hence s=703920/(908.2-96)=866.68 j/kg-k

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