   Chapter 11, Problem 30P

Chapter
Section
Textbook Problem

A 50.-kg ice cube at 0°C is heated until 45 g has become water at 100.°C and 5.0 g has become steam at 100.°C. How much energy was added to accomplish the transformation?

To determine
The energy required to accomplish the transformation.

Explanation

Given Info: Mass of ice cube is 50 g, initial temperature of ice cube is 0°C , mass of water is 45 g and initial temperature of water is 0°C , and final temperature of water is 100°C .

Energy supplied must melt the ice to cold water at 0°C , then it has to raise the temperature of water to 100°C , then transform the water to steam at 100°C .

Formula to calculate the heat required to melt the ice to cold water is,

Qmelt=miceLf (1)

• Qmelt is the energy required to melt the ice to cold water,
• mice is the mass of the ice,
• Lf is the latent heat of fusion of ice,

Formula to calculate the heat required to raise the temperature of cold water to hot water at 100°C is,

Qboil=mwatercwater(TfTi,water) (2)

• Qboil is the heat required to raise the temperature of cold water to hot water.
• cwater is the specific heat of water,
• Ti,water is the initial temperature of cold water from ice,
• Tf is the boiling temperature of water,

Formula to calculate the heat required to transform 5 g of water to steam at 100°C is,

Qsteam=msteamLv (3)

• Qsteam is the energy required to transform 5 g water to steam,
• msteam is the mass of the steam,
• Lv is the latent heat of vaporization,

Formula to calculate the energy required to accomplish the transformation is,

Qtran=Qmelt+Qboil+Qsteam (4)

Substitute equation (1), (2), (3) in equation (4) to calculate Qtran .

Qtran=miceLf+msteamLv+mwatercwater(TfTi,water)

Substitute 50 g for mice , 3

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