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An ideal monatomic gas initially has a temperature of 338 K and a pressure of 6.96 atm. It is to expand from volume 435 cm3 to volume 1310 cm3. If the expansion is isothermal, what are (a) the final pressure (in atm) and (b) the work done by the gas? If, instead, the expansion is adiabatic, what are (c) the final pressure (in atm) and (d) the work done by the gas?

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  1. (a) In an isothermal expansion,
    P*V = constant = Po*Vo
    P(final)/Po = Vo/V(final)
    = 435/1310 = 0.332

    Use that and the initial pressure to get the final pressure.
    (b) Work done by gas =
    Integral of P*dV = (Po*Vo)*Integral dV/V
    = Po*Vo ln(1310/435)
    Make sure P is in units of Pascals, and Volume in m^3, to get work in Joules.

    (c) For adiabatic expansion of a monatomic gas,
    P*V^(5/3) = constant = Po*Vo^(5/3)
    Pfinal/Po = (0.332)^5/3 = 0.159

    (d) Calculate the P*dV integral again, this time using the adiabatic relationship for P(V).

    P (V) = [Po*Vo^(5/3)]/V^5/3

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