Work problem -- Steam piston volume and work length

[snowwhite]

Homework Statement

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.

Homework Equations

P1V1^(1.135)= P2V2^(1.135)

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

 

[Dr.D]

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?

 

[snowwhite]

The exponent is 1.135
Sorry about that

 

[snowwhite]

How to calculate the Work done in a isobaric process piston?