Soda from a m_s = 12oz can at a temperature T_s = 18.5 deg C is poured in its en

Question

Soda from a m_s = 12oz can at a temperature T_s = 18.5 deg C is poured in its entirety into a glass containing a mass m_I = 0.16 kg amount of ice at temperature T_I = 17.5 deg C. Assume that ice and water have the following specific heats: c_I = 2090 J/(kg deg C) and c_s = 4186 J/(kg deg C), and the latent heat of fusion of ice is L_f = 334 kJ/kg.

A. In degrees Celsius, what is the final temperature T_final of the mixture?

B. Write an expression for how much of the ice m_melted has melted.

C. In kilograms, how much of the ice m_melted has melted

Explanation / Answer

A) Let final temperature be 0 degree C (proved later)

Let x kg ice melts.

Heat lost = Heat gained

B) m_I*c_I*(0-T_I) + x*L_f = c_s*m_s*T_s

C) 0.16*2090*17.5 + 334000x = 4186*0.3402*18.5

x = (4186*0.3402*18.5 - 0.16*2090*17.5)/334000

= 0.0613 kg which is less than 0.16kg

Hence our assumption as Tf=0C is correct

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