Question

An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C....

An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 402-g sample of silver at an initial temperature of 86°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup.

Homework Answers

Answer #1

Mass of aluminium cup = ma

Mass of water = mw = 225 g = 0.225 kg

Mass of copper stirrer = mc = 40 g = 0.04 kg

Mass of silver sample = ms = 402 g = 0.402 kg

Initial temperature of aluminium, water and copper = T1 = 27 oC

Initial temperature of silver sample = T2 = 86 oC

Final temperature of the mixture = T = 32 oC

Specific heat of aluminium = Ca = 910 J/(kg.K)

Specific heat of water = Cw = 4186 J/(kg.K)

Specific heat of copper = Cc = 390 J/(kg.K)

Specific heat of silver = Cs = 230 J/(kg.K)

The heat lost by the silver is gained by aluminium, water and copper.

msCs(T2 - T) = maCa(T - T1) + mcCc(T - T1) + mwCw(T - T1)

(0.402)(230)(86 - 32) = ma(910)(32 - 27) + (0.04)(390)(32 - 27) + (0.225)(4186)(32 - 27)

ma = 0.0452 kg

ma = 45.2 grams

Mass of the aluminium cup = 45.2 grams

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