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15 October, 14:30

A 4.40 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.121 m3 to 0.60 m3. initially the pressure was 1.00 atm. (assume no molecular vibration.) (a) determine the initial and final temperatures.

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  1. 15 October, 18:26
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    First, we have to get Pf from this formula:

    Pf = Pi * (Vi/Vf) ^γ

    when Pi = 1 atm = 1 * 1.01325 x 10^5 Pa

    Vi = 0.121 m^3

    Vf = 0.6 m^3

    and gamma γ = 1.4

    by substitution:

    ∴ Pf = 1 atm * (0.121 / 0.6) ^1.4

    = 0.11 atm = 11145.75 Pa

    a) to get initial T:

    when Pivi = nRTi

    by substitution

    (1.01325 x 10^5) * 0.121 = 4.4 * 8.31 * Ti

    ∴Ti = 335 K

    b) to get Tf:

    PfVf = nRTf

    by substitution:

    11145.75 * 0.6 = 4.4 * 8.31 * Tf

    ∴ Tf = 183 K
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