   Chapter 11, Problem 19P

Chapter
Section
Textbook Problem

# An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 400-g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup.

To determine
The mass of the aluminum cup.

Explanation

Given Info: mass of copper stirrer is 40 g, mass of the water is 225 g, initial temperature of the stirrer and water pellet is 27°C , mass of silver is 400 g, initial temperature of the silver is 87°C , and final equilibrium temperature is 32°C .

Formula to calculate Heat gained by water is,

QW=mWcW(TfTiW)

• QW is the heat gained by water,
• mW is the mass of water,
• cW is the specific heat of water,
• TiW is the initial temperature of water,
• Tf is the final temperature of water,

Formula to calculate Heat gained by stirrer is,

QCu=mCucCu(TfTiCu)

• QCu is the heat gained by copper stirrer,
• mCu is the mass of stirrer,
• cCu is the specific heat of copper,
• TiCu is the initial temperature of stirrer,

Formula to calculate Heat gained by aluminum cup is,

QAl=mAlcAl(TfTiAl)

• QAl is the heat gained by aluminum cup,
• mAl is the mass of aluminum,
• cAl is the specific heat of aluminum,
• TiAl is the initial temperature of aluminum

Formula to calculate Heat lost by silver is,

QAg=mAgcAg(TfTiAg)

• QAg is the heat lost by silver,
• mAg is the mass of silver,
• cAg is the specific heat of silver,
• TiAg is the initial temperature of silver,

Heat gained by the water is heat lost by the pellet.

QW+QCu+QAl=QAg

Use mWcW(TfTiW) for QW , mCucCu(TfTiCu) for QCu , mAlcAl(TfTiAl) for QAl , and mAgcAg(TfTiAg) for QAg and rewrite in terms of mAl

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