Concept explainers
A 0.3-L glass of water at 20°C is to be cooled with ice to 5°C. Determine how much ice needs to be added to the water, in grams, if the ice is at (a) 0°C and (b) −20°C. Also determine how much water would be needed if the cooling is to be done with cold water at 0°C. The melting temperature and the heat of fusion of ice at atmospheric pressure are 0°C and 333.7 kJ/kg, respectively, and the density of water is 1 kg/L.
(a)
The amount of ice that needs to be added into water at 0 C of temperature.
Answer to Problem 134RP
The amount of ice that needs to be added into water at 0 C of temperature is
Explanation of Solution
Write the expression for the mass of the water.
Here, the density of the water is
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Simplify Equation (II) and write energy balance relation of cold water
Here, the heat to be transfer into the system is
Conclusion:
Substitute 0 for
Here, the mass of the ice is
From the Table A-3 “Properties of common liquids, solids and foods”, obtain the value of specific heat of ice at 0 C and room temperature as
Substitute
For initial temperature of ice as 0 C.
Substitute
Thus, the amount of ice that needs to be added into water at 0 C of temperature is
(b)
The amount of ice that needs to be added into water at -20 C of temperature.
The amount of water that needs to cool down the cold water at 0 C of temperature.
Answer to Problem 134RP
The amount of ice that needs to be added into water at -20 C of temperature is
The amount of water that needs to cool down the cold water at 0 C of temperature is
Explanation of Solution
Substitute 0 for
Here, the mass of cold water is
Conclusion:
For initial temperature of ice as -20 C instead of 0 C.
Substitute
Thus, the amount of ice that needs to be added into water at -20 C of temperature is
Substitute
Thus, the amount of water that needs to cool down the cold water at 0 C of temperature is
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Chapter 4 Solutions
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