The drawing shows an ideal gas confined to a cylinder by a masslesspiston that i

Question

The drawing shows an ideal gas confined to a cylinder by a masslesspiston that is attached to an ideal spring. Outside the cylinder isa vacuum. The cross-sectional area of the piston is A =2.50 × 10-3 m2. The initial pressure,volume, and temperature of the gas are, respectively,P0, V0 = 6.00 ×10-4 m3 and T0 = 273 K,and the spring is initially stretched by an amountx0 = 0.097 m with respect to its unstrainedlength. The gas is heated, so that its final pressure, volume, andtemperature are Pf, Vf andTf and the spring is stretched by an amountxf = 0.12 m with respect to its unstrainedlength. What is the final temperature of the gas?

Explanation / Answer

   the final volume is the initial volume plus theamount by which the volume increases as the spring stretches
   the increased volume due to the additionalstretching is
   A (xf - xo)
   so we get that
   Vf = Vo + A (xf- xo)
   the final temperature canb be obtained from
   Tf = (Pf Vf /Po Vo) To
    into this result we can now substituteexpressions for Po and Pf
    Po A = k xo
    Pf A = k xf
    Tf = (Pf Vf /Po Vo) To
    = (k xf / A)[Vo + A(xf - xo)]To /(k xo / A) Vo
        = xf[Vo + A(xf - xo)] To /xo Vo
= ........... K

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