Question

What mass of ice would it take to lower the temperature of 0.5kg of water from 20°C to 0°C. 7. A 100-g piece of iron is heated to 100°C and then dropped into a cavity in a large block of ice at 0°C. How much mass of ice will melt? 8. 50 grams of hot water at 80°C is poured into a cavity in a very large block of ice at 0°C. The final temperature of the water in the cavity is then O°C. Show that the mass of ice that melts is 50 grams. 9. 10. Before the invention of refrigerators, people used ice boxes to keep food cool. How much heat would a 50 kg block of ice remove from food in an ice box by the time the ice was completely melted? 11. In question 10, did all the heat absorbed by the ice come from the food? What other substances transfer heat to the ice? 12. The heat of vaporization of ethyl alcohol is about 8.46 x 205 J/kg. Show that if 2 kg of this refrigerant were allowed to vaporize in a refrigerator, it could freeze 5kg of 0°C water to ice.

Answer 1

Here we use principal of calorimetry,which states"Neglecting any heat exchange with surrounding,the total heat given by the hot objects equals the heat received by the cold objects."

Latent heat of fusion of ice, L_I = 3.4 times 10^5 J/kg specific heat capacity of water, s_w = 4200 J/kg - k Given that, mass of water = 0.5 kg rightarrow m_w Temperature difference = 20 - 0 = 20 degree c = Delta T Therefore Heat released as water cool down = m_w s_w Delta T = 0.5 times 4200 times 20 = 42000 J = 42 k J Let this heat, melt the ice of mass m_i Therefore 42000 = m_i L_i = (3.4 times 10^5) m_i or m m_i = 42000/3.5 times 10^5 = 0.12 kg