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18 June, 09:07

2.0 mol of monatomic gas A initially has 5000 J of thermal energy. It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy. (4+4 pts.) a. What is the average energy per atom at equilibrium? b. Find the equilibrium temperature.

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  1. 18 June, 11:04
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    E_particle = 1,129 10⁻²⁰ J / particle

    T = 817.5 K

    Explanation:

    Energy is a scalar quantity so it is additive, let's look for the total energy of each gas

    Gas a

    E_a = 2 5000 = 10000 J

    Gas b

    E_b = 3 8000 = 24000 J

    When the total system energy is mixed it is

    E_total = E_a + E_b

    E_total = 10000 + 24000 = 34000

    The total mass is

    M = m_a + m_b

    M = 2 + 3 = 5

    The average energy among the entire mass is

    E_averge = E_total / M

    E_averago = 34000/5

    E_average = 6800 J

    One mole of matter has Avogadro's number of atoms 6,022 10²³ particles

    Therefore, each particle has an energy of

    E_particle = E_averag / 6.022 10²³ = 6800 / 6.022 10²³

    E_particle = 1,129 10⁻²⁰ J / particle

    For find the temperature let's use equation

    E = kT

    T = E / k

    T = 1,129 10⁻²⁰ / 1,381 10⁻²³

    T = 8.175 102 K

    T = 817.5 K
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