Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 14, Problem 53P
To determine

The mass of the ice added to cool the coffee.

Expert Solution & Answer
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Answer to Problem 53P

The mass of the ice added to cool the coffee is 36g.

Explanation of Solution

Heat flows from coffee to the ice is taken as positive, when it enters the ice to melt it and warm the melt water, and as taken as negative when it leaves from the coffee.

The sum of the heat flow into the ice to cool the coffee is equal to zero.

Qice+QC=0 (I)

Here, Qice is the amount of heat lost by the ice and QC is the amount of heat gained by the coffee.

Write the equation for the amount of heat energy lost by the ice

Qice=micecwΔTice (II)

Here, mw is the mass of the water, cw is the specific heat capacity of the water, and ΔTice is the change in temperature of ice cools.

Write the equation for latent heat of fusion (ice melts).

Qice=miceLf (III)

Here, mice is the mass of the ice melts, and Lf is the latent heat of fusion for ice melts.

Write the equation for the amount of heat energy gained by the cool coffee

QC=mCcwΔTC (IV)

Here, mC is the mass of the coffee, cw is the specific heat capacity of the water, and ΔTC is the change in temperature of the coffee gets cooled.

Conclusion:

Substitute the equation (II), (III) and (IV) in equation (I) to solve for mice.

miceLf+micecwΔTice+mCcwΔTC=0mice(Lf+cwΔTice)+mCcwΔTC=0mice(Lf+cwΔTice)=mCcwΔTCmice=mCcwΔTCLf+cwΔTice

Substitute 250g for mC, 4186J/kgK for cw, 80.0°C60.0°C for ΔTC, 0°C60.0°C for ΔTice, and 333.7kJ/kg for Lf in above equation.

mice=(250g)(0.001kg1g)(4186J/kgK)[(80.0K+273.15K)(60.0K+273.15K)](333.7kJ/kg)(103J1kJ)+(4186J/kgK)[(0K+273.15K)(60.0K+273.15K)]=(0.250kg)(4186J/kgK)(193.15K213.15K)(333.7×103J/kg)+(4186J/kgK)(273K213.15K)=(0.250kg)(4186J/kgK)(20K)(333.7×103J/kg)+(4186J/kgK)(60K)

Solve the above relation for mice in gram.

mice=20930J584860J/kg=0.036kg(1000g1kg)=36g

Therefore, the mass of the ice added to cool the coffee is 36g.

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Chapter 14 Solutions

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