Three liquids are at temperatures of 9 ◦C, 24◦C, and 30◦C, respectively. Equal masses of the first two liquids are mixed, and the equilibriu

Question

Three liquids are at temperatures of 9 ◦C, 24◦C, and 30◦C, respectively. Equal masses of the first two liquids are mixed, and the equilibrium temperature is 15◦C. Equal masses of the second and third are then mixed, and the equilibrium temperature is 26.2 ◦C.

Find the equilibrium temperature when equal masses of the first and third are mixed.
Answer in units of ◦C

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RI SƠ 9 mins 2021-07-22T11:24:14+00:00 1 Answers 0 views 0

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    2021-07-22T11:25:18+00:00

    Answer:

    14.8°C

    Explanation:

    When the first two are mixed:

    m C₁ (T₁ − T) + m C₂ (T₂ − T) = 0

    C₁ (T₁ − T) + C₂ (T₂ − T) = 0

    C₁ (9 − 15) + C₂ (24 − 15) = 0

    -6 C₁ + 9 C₂ = 0

    C₁ = 1.5 C₂

    When the second and third are mixed:

    m C₂ (T₂ − T) + m C₃ (T₃ − T) = 0

    C₂ (T₂ − T) + C₃ (T₃ − T) = 0

    C₂ (24 − 26.2) + C₃ (30 − 26.2) = 0

    -2.2 C₂ + 3.8 C₃ = 0

    C₂ = 1.73 C₃

    Substituting:

    C₁ = 1.5 (1.73 C₃)

    C₁ = 2.59 C₃

    When the first and third are mixed:

    m C₁ (T₁ − T) + m C₃ (T₃ − T) = 0

    C₁ (T₁ − T) + C₃ (T₃ − T) = 0

    (2.59 C₃) (9 − T) + C₃ (30 − T) = 0

    (2.59) (9 − T) + 30 − T = 0

    23.3 − 2.59T + 30 − T = 0

    3.59T = 53.3

    T = 14.8°C

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