   Chapter 11, Problem 39P

Chapter
Section
Textbook Problem

Steam at 100.°C is added to ice at 0°C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 10. g and the mass of ice is 50. g. (b) Repeat with steam of mass 1.0 g and ice of mass 50. g.

(a)

To determine
The amount of ice melted and the final temperature when the mass of steam is 10 g.

Explanation

Given Info: Mass of ice is 50 g, mass of steam is 10 g, initial temperature of ice is 0°C , initial temperature of steam is 100°C ,

Explanation:

Formula to calculate the energy required to melt 50 g of ice is,

QA=miceLf

• QA is the heat required to melt 50 g of ice,
• mice is the mass of ice,
• Lf is the latent heat of fusion of ice,

Substitute 50 g for mice and 333kJ/kg for Lf to find QA .

QA=(50g)(103kg1g)(333kJ/kg)=16650J(103kJ1J)17kJ

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

Qmelt=miceLf (I)

• 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 is,

Qboil=micecwater(Tf,Ti,ice) (II)

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

Formula to calculate the heat lost by the steam when it condensed to hot water at 100°C is,

Qsteam=msteamLv (III)

• Qsteam is the energy given out when steam condenses to water,
• msteam is the mass of the steam,
• Lv is the latent heat of vaporization,

Formula to calculate the heat lost by the steam to reduces its temperature from 100°C to equilibrium temperature is,

Qsteam=msteamcsteam(TfTi,steam) (IV)

• Qsteam is the heat lost by the steam to reduces its temperature from 100°C to equilibrium temperature,
• msteam is the mass of steam,
• csteam is the specific heat of steam,
• Ti,steam is the initial temperature of steam,

Energy supplied by the steam when it condenses to water at 100°C and then reduces it temperature to Tf . This energy is gained melts the ice to cold water at 0°C , then it has to raise the temperature of water to to Tf .

Qmelt+Qboil=QsteamQsteam (V)

Substitute equation (I), (II), (III) (IV) in equation (V) to calculate Tf

(b)

To determine
The amount of ice melted and the final temperature when the mass of steam is 1.0 g.

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