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?

 

[DeeNos]

= 0.1266 KJ

I would like to offer a few suggestions to improve the solution provided. First, it would be helpful to label the equations used and explain how they were derived. Additionally, it would be beneficial to explicitly state the units for each value and the final answer. Lastly, I would recommend checking the calculations for accuracy and rounding to an appropriate number of significant figures. Overall, the solution provided is a good start, but could benefit from further explanation and clarity.