The boy filled a glass with a capacity of 200 cm³ with ¾ boiling water (temperature = 100⁰С) and added cold water to its full volume. Find the established water temperature if the cold water temperature is 20⁰С.
Given: V (glass volume) = 200 cm3; t1 (boiling water temperature) = 100 ºС; V1 (volume of boiled water in a glass) = 0.75V; V2 (volume of cold water in a glass) = 0.25V; t2 (cold water temperature) = 20 ºС.
We determine the temperature that is established in the glass from the equality:
С * ρ * V1 * (t1 – t) = С * ρ * V2 * (t – t2).
0.75V * (t1 – t) = 0.25V * (t – t2).
0.75 * (t1 – t) = 0.25 * (t – t2).
0.75 * (100 – t) = 0.25 * (t – 20).
75 – 0.75t = 0.25t – 5.
t = 80 ºС.
Answer: The temperature in the glass is 80 ºС.
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