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On a hot summer day, you decide to make some iced tea. First, you brew 1.50 LL of hot tea and leave it to steep until it has reached a temperature of TteaTteaT_tea = 75.0 ∘C∘C. You then add 0.975 kgkg of ice taken from the freezer at a temperature of TiceTiceT_ice = 0 ∘C∘C. By the time the mix reaches equilibrium, all of the ice has melted. What is the final temperature TfTfT_f of the mixture?

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Explanation:

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The final temperature of the mixture is 13.9°C

Thermal equilibrium:

By the time the ice and the coffee reach an equilibrium temperature, the heat gained by the ice must be equal to the heat lost by the tea.

Let the final temperature of the system be T, then:

the heat energy gained by ice = heat required to convert ice to water + heating of water till temperature T

the heat gained by the ice

ΔQ = mL + mcΔT

ΔQ = 0.975×336 + 0.975×419×(T-0)    ...............(i)

the heat gained by the tea

mass =  volume×density = 1000×1.5

ΔQ = mcΔT

ΔQ = 1000×1.5×4.19×(T-75)     ..............(ii)

from (i) and (ii) we get:

0.975×336 + 0.975×419×(T-0) = 1000×1.5×4.19×(T-75)

solving the above equation we get:

T = 13.9°C

Learn more about thermal equilibrium:

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