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11 October, 00:58

2.3mol of monatomic gas A initially has 4700J of thermal energy. It interacts with 2.6mol of monatomic gas B, which initially has 8500J of thermal energy.

Which gas has the higher initial temperature?

Gas A or B?

1-What is the final thermal energy of the gas A?

2-What is the final thermal energy of the gas B?

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Answers (1)
  1. 11 October, 01:26
    0
    Gas B has the higher initial temperature

    6,199 J

    7,008 J

    Explanation:

    Mathematically;

    The thermal energy of a gas is given by:

    E = 3/2 n kT

    Where n is the number of moles, K is the molar gas constant and T is the temperature

    For Gas A;

    4700 = 1.5 * 2.3 * 8.31 * T

    T = 4700/28.6695

    Thus, T = 163.94 K

    For gas B

    8500 = 1.5 * 2.6 * 8.31 * T

    T = 8500/32.409

    T = 262.27 K

    This means that gas B has a higher temperature than gas A.

    At equilibrium, temperature

    T = naTa + nbTb / (na + nb)

    T = [2.3 (163.94) + 2.6 (262.27) ] / (2.3 + 2.6)

    T = [377.062 + 681.902]/4.9 = 216.12 K

    216.12 K is the equilibrium temperature

    = 216.12 K is the equilibrium temperature.

    Thus, final thermal energy of Gas A and B

    Gas A = 1.5 * 2.3 * 8.314 * 216.12 = 6,199 J

    Gas B = 1.5 * 2.6 * 8.314 * 216.12 = 7,008 J
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