   Chapter 11, Problem 29P

Chapter
Section
Textbook Problem

A 75-g ice cube al 0°C is placed in 825 g of water at 25°C. What is the final temperature of the mixture?

To determine
The final temperature of the mixture.

Explanation

Given Info: Mass of ice 75 g, initial temperature of ice is 0°C , mass of water is 825 g and initial temperature of water is 25°C .

Part of Heat energy from water melts the ice to water at 0°C and remaining heat energy raises the temperature of the cold water. Heat lost be warm water is equal to heat gained by cold water.

Formula to calculate the heat gained by cold water is,

Qcold=miceLf+micecwater(TfTi,ice)

• Qcold is the energy gained by cold water from ice,
• mice is the mass of the ice,
• Lf is the latent heat of ice,
• cwater is the specific heat of water,
• Ti,ice is the initial temperature of cold water from ice,
• Tf is the final temperature of the mixture,

Formula to calculate the heat lost by warm water is,

Qwarm=mwatercwater(TfTi,water)

• Qwarm is the energy lost by warm water,
• mwater is the mass of warm water,
• Ti,water is the initial temperature of warm water,

Heat lost by warm water is equal to the Heat gained by cold water from ice.

Qcold=Qwarm

Use miceLf+micecwater(TfTi,ice) for Qcold and mwatercwater(TfTi,water) for Qwarm to find Tf .

miceLf+micecwater(TfTi,ice)=mwatercwater(TfTi,water)miceLf+micecwaterTfmicecwaterTi,ice=mwatercwaterTf+mwatercwaterTi,watermicecwaterTf+mwatercwaterTf=mwate

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