To determine The minimum mass of ice that could be added to the water to ends up with a final temperature of 0 ° C . Explanation Write the equation for the energy extracted when the water is cooled to 0 ° C . Q ′ 2 = m water c water ( T f water − T i water ) (I) Here, Q ′ 2 is the amount of energy extracted when the water is cooled down to 0 ° C , m water is the mass of water initially present, c water is the specific heat capacity of water, T f water is the final temperature of water, T i water is the initial temperature of water. The value of c water is 4.184 kJ/kg ⋅ K . Write the equation for the energy needed to raise the temperature of ice to 0 ° C . Q 1 = m ice c ice ( T f ice − T i ice ) (II) Here, Q 1 is the amount of energy needed to heat the ice to 0 ° C , m ice is the mass of ice, c ice is the specific heat capacity of ice, T f ice is the final temperature of ice, T i ice is the initial temperature of ice. Write the equation for the energy needed to melt the ice at 0 ° C . Q 2 = m ice L f (III) Here, Q 2 is the energy needed to melt the ice, L f is the latent heat of fusion of ice. Write the equation for the total energy needed. Q = Q 1 + Q 2 (IV) Here, Q is the total energy needed. Put equations (II) and (III) in the above equation to find the expression for Q . Q = m ice c ice ( T f ice − T i ice ) + m ice L f = m ice ( c ice ( T f ice − T i ice ) + L f ) (V) The energy extracted from the water to cool it down to 0 ° C must be equal to the total energy needed to melt the ice. Q ′ 2 = Q Put equation (3) in the above equation. Q ′ 2 = m ice ( c ice ( T f ice − T i ice ) + L f ) Rewrite the above equation for m ice . m ice = Q ′ 2 ( c ice ( T f ice − T i ice ) + L f ) (VI) The value of c ice is 2

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Chapter 17, Problem 32E

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The minimum mass of ice that could be added to the water to ends up with a final temperature of 0°C.

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Chapter 17, Problem 31E

Chapter 17, Problem 33E

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Chapter 17 Solutions

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