Iced tea is made by adding ice to 1.9 kg of hot tea,initially at 90.0°C.How many kg of ice,initially at 0°C,are required to bring the mixture to 15.0°C? (L_f = 3.33 × 10⁵ J/kg,c_w = 4 186 J/kg⋅°C)

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat released by the tea as it cools down from 90.0°C to 15.0°C:

Q1 = m1c1ΔT1
Q1 = 1900 g × 4.186 J/g·°C × (90.0°C - 15.0°C)
Q1 = 695,484 J

Next, we need to calculate the amount of heat absorbed by the ice as it melts and then warms up to 15.0°C:

Q2 = m2c2ΔT2 + m2L
Q2 = m2(4.186 J/g·°C)(15.0°C - 0°C) + m2(333 J/g)
Q2 = m2(69,804 J/kg)

Since the ice melts at 0°C, we know that m2 = Q1 / L:

m2 = Q1 / L
m2 = 695,484 J / (333 J/g)
m2 = 2,086 g = 2.1 kg

Therefore, the answer is (C) 1.5 kg.

Iced Tea Is Made by Adding Ice to 1