Iced tea is made by adding ice to 1.7 kg of hot tea,initially at 85°C.How many kg of ice,initially at 0°C,are required to bring the mixture to 10°C? (L_f = 3.33 × 10⁵ J/kg,c_w = 4 186 J/kg⋅°C)

Question

Quizplus · Accepted Answer

To bring the mixture from 85°C to 10°C, the amount of heat lost by the tea will be equal to the amount of heat gained by the ice. Using the equation Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature:

Heat lost by tea = Heat gained by ice
mTeacTea(ctea)ΔTea = mIceciceΔTice

Rearranging for mIce, we get:

mIce = (mTea ctea ΔTea)/(cice ΔTice)

Substituting the given values, we obtain:

mIce = (1.7 kg)(4186 J/kg⋅°C)(85°C - 10°C)/(3330 J/kg) ≈ 1.4 kg

Therefore, the answer is C, 1.4 kg of ice.

Iced Tea Is Made by Adding Ice to 1