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Work problem -- Steam piston volume and work length

  1. Nov 13, 2014 #1
    1. The problem statement, all variables and given/known data

    Steam is raised as saturated steam at 6 bar (g) and supplied to the first ( high pressure ) piston. The steam then exhausts from piston 1 at 3 bar (g).
    The steam is thought to expand adiabatically in accordance with
    PV^( 135 .1)= Constant
    Given the initial volume is 3.54×10-4 m3 and the diameter of the piston is 50 mm, a) calculate the final volume for the 6 bar piston and the stroke lenght.

    b) Calculate the work done by the steam in the high pressure piston per stroke.
    2. Relevant equations
    P1V1^(1.135)= P2V2^(1.135)

    3. The attempt at a solution
    From which: V2= V1(P1/P2)^(1/1.135)=(3.54x10^-4 metres cube)(600 KPa/300 KPa)^(1/1.135)=6.51x(10^-4) metres cube

    stroke length? V2= length x pi(0.025)(^2)
    so: length= V2/(pi)(0.025)(^2)=(6.51x10^-4)/pi(0.025)(^2)=0.33 m

    b) Work done= P1V1-P2V2/(n-1)=(6x10^5)(3.54x10^-4)-(3x10^5)(6.51x10^-4)/1.135-1=126.6 Nm= 0.1266 KJ
    c)total change in internal energy of system per expansion stroke
    internal energy= q+w=0+0.1266 KJ
  2. jcsd
  3. Nov 13, 2014 #2
    So, is there a question?

    I see one problem, however. In the initial statement of the problem, the polytropic exponent is given as 1351, but in your problem solution, you have used 1.135; which is it?
  4. Nov 13, 2014 #3
    The exponent is 1.135
    Sorry about that
  5. Nov 14, 2014 #4
    How to calculate the Work done in a isobaric process piston?
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