   Chapter 11, Problem 31P

Chapter
Section
Textbook Problem

A 100.-g cube of ice at 0°C is dropped into 1.0 kg of water that was originally at 80.°C. What is the final temperature of the water after the ice has melted?

To determine
The final temperature of the water after the ice has melted.

Explanation

Given Info: Mass of ice cube is 100 g, initial temperature of ice is 0°C , mass of water is 1.0 kg and initial temperature of water is 80°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+mwater<

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