   Chapter 11, Problem 25P

Chapter
Section
Textbook Problem

A Styrofoam cup holds 0.275 kg of water at 25.0°C. Find the final equilibrium temperature after a 0.100-kg block of copper at 90.0°C is placed in the water. Neglect any thermal energy transfer with the Styrofoam cup.

To determine
The final equilibrium temperature.

Explanation

Given Info: Mass of water is 0.275 kg, Initial temperature of water is 25.0°C , mass of copper is 0.100 kg, and initial temperature of copper is 90.0°C .

The heat lost by the copper is equal to the heat gained water.

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 lost by copper block is,

QCu=mCucCu(TfTiCu)

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

The heat lost by the copper block is equal to the heat gained by water.

QW=QCu

Use mAlcAl(TfTiAl) for QAl and mCucCu(TfTiCu) for QCu mWcW(TfTiW) to rewrite in terms of Tf .

mWcW(TfTiW)=mCucCu(TfTiCu)mWcWTfmWcWTiW=mCucCuTf+m</

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