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21 March, 08:00

A gas is compressed from an initial volume of 5.40 L to a final volume of 1.20 L by an external pressure of 1.00 atm. During the compression the gas releases 128 J of heat. Part A What is the change in internal energy of the gas?

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  1. 21 March, 08:26
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    296.2J

    Explanation:

    From the first law, you should know that the change in internal energy of a system is given by:

    ΔE = q + w

    where q is the heat added to the system (q is negative if heat is released from the system)

    and w is the work done on the system by the surroundings.

    We are told that q = - 128 J.

    Because the volume of the system decreases, the surroundings are doing work on the system, so w will be positive. If the compression is done "quasistatically", so that the internal pressure of the system is always infinitesimally close to the external pressure, then the work done is w = p*ΔV

    1 atm = 1.01*10^5 Pa, and 1 liter = 10^-3 m^3, so:

    w = (1.01^10^5 N/m^2) * (5.40 - 1.20) * 10^-3 m^3

    w = 424.2 J

    The change internal energy is then:

    ΔE = - 128 J + 424.2J = + 296.2 J
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