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8 January, 13:50

Consider the following cyclic process carried out in two steps on a gas. Step 1: 50. J of heat is added to the gas, and 20. J of expansion work is performed. Step 2: 62 J of heat is removed from the gas as the gas is compressed back to the initial state. Calculate the work for the gas compression in Step 2.

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  1. 8 January, 14:13
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    the work for the gas compression in step 2 = 32 J

    Explanation:

    Given that:

    A system usually comes back to initial state after 2 steps;

    That implies:

    ΔE₁ + ΔE₂ = 0

    When heat is added to a given system, q tends to be positive

    q is also negative when the heat is removed from the system

    The work (W) when expansion occurs is said to be negative and positive when compression occurs.

    ∴ ΔE₁ = q₁ + W₁

    ΔE₁ = 50 J + (-20 J)

    ΔE₁ = 30 J

    ΔE₂ = q₂ + W₂

    ΔE₂ = - 62 J + W₂

    ΔE₁ + ΔE₂ = 0

    30 J - 62 J + W₂ = 0

    W₂ = - 30 J + 62 J

    W₂ = 32 J

    Thus, the work for the gas compression in step 2 = 32 J
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