A 43.9-g piece of copper (CCu= 0.385 J/g°C) at 135.0°C is plunged into 254 g of water at 39.0°C. Assuming that no heat is lost to the surrou

Question

A 43.9-g piece of copper (CCu= 0.385 J/g°C) at 135.0°C is plunged into 254 g of water at 39.0°C. Assuming that no heat is lost to the surroundings, what will the final temperature of the system be?

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Ngọc Hoa 3 years 2021-08-24T04:10:12+00:00 2 Answers 85 views 0

Answers ( )

  1. dangkhoa
    0
    2021-08-24T04:11:30+00:00
    Reply

    Answer:

    40.497 °C

    Explanation:

    Heat lost by copper = heat gained by water

    CM(T₁-T₃) = cm(T₃-T₂)…………………… Equation 1

    Where C = specific heat capacity of copper, M = mass of copper, T₁ = Initial Temperature of copper, T₂ = Initial Temperature of water, T₃ = final temperature of the system,

    Make T₃ the subject of the equation

    T₃= (CMT₁+cmT₂)/(CM+cm)…………….. Equation 2

    Given: C = 0.385 J/g°C, M = 43.9 g, c = 4.2 J/g°C, m = 254 g, T₁ = 135 °C, T₂ = 39 °C

    Substitute into equation 2

    T₃ = (0.385×43.9×135+4.2×254×39)/(0.385×43.9+4.2×254)

    T₃ = (2281.70+41605.2)/(16.9015+1066.8)

    T₃ = 43886.9/1083.7015

    T₃ = 40.497 °C.

    Hence the final temperature of the system = 40.497 °C

  2. thucuc
    0
    2021-08-24T04:11:56+00:00
    Reply

    Answer:

    T = 40.501\,^{\textdegree}C

    Explanation:

    The interaction of the piece of copper and water means that the first one need to transfer heat in order to reach a thermal equilibrium with water. Then:

    -Q_{out,Cu} = Q_{in,H_{2}O}

    After a quick substitution, the expanded expression is:

    -(43.9\,g)\cdot (0.385\,\frac{J}{g\cdot ^{\textdegree}C} )\cdot (T-135^{\textdegree}C) = (254\,g)\cdot (4.187\,\frac{J}{g\cdot ^{\textdegree}C} )\cdot (T-39\,^{\textdegree}C)

    -16.902\,\frac{J}{^{\textdegree}C}\cdot (T-135^{\textdegree}C) = 1063.498\,\frac{J}{^{\textdegree}C} \cdot (T-39^{\textdegree}C)

    43758,192\,J = 1080.4\,\frac{J}{^{\textdegree}C}\cdot T

    The final temperature of the system is:

    T = 40.501\,^{\textdegree}C

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