To find out how much ice remains when the system reaches equilibrium, we need to calculate the total heat gained and lost during the process. Here's a step-by-step approach to solve the problem:
1. Calculate the heat lost by the ice to reach 0°C:
Heat lost = mass of ice * heat of fusion
Heat lost = 250 g * 79.7 cal/g
Heat lost = 19925 cal
2. Calculate the heat gained by the ice from 0°C to the final temperature:
Heat gained = mass of ice * specific heat * temperature change
Heat gained = 250 g * 0.5 cal/g°C * 18°C
Heat gained = 2250 cal
3. Calculate the heat gained by the water to reach equilibrium:
Heat gained = mass of water * specific heat * temperature change
Heat gained = 600 g * 1 cal/g°C * (0°C - 18°C)
Heat gained = -10800 cal (negative sign indicates heat loss)
4. Total heat gained = Heat gained by ice (2250 cal) + Heat gained by water (-10800 cal)
Total heat gained = -8550 cal
5. Since the system is insulated, the total heat lost by the ice is equal to the total heat gained by the system:
Total heat lost = Heat lost by ice (19925 cal) + Total heat gained (-8550 cal)
Total heat lost = 11375 cal
6. Determine how much ice remains by converting the total heat lost to mass of ice:
Mass of ice remaining = Total heat lost / Heat of fusion
Mass of ice remaining = 11375 cal / 79.7 cal/g
Mass of ice remaining ≈ 142.6 g
Therefore, approximately 142.6 g of ice remains when the system reaches equilibrium.
