# Work problem -- Steam piston volume and work length

• snowwhite
In summary, the problem involves a steam system with a high pressure piston that is supplied with saturated steam at 6 bar and exhausts at 3 bar. The steam expands adiabatically according to the equation PV^(1.135) = constant. The initial volume and diameter of the piston are given, and the final volume and stroke length are calculated. The work done by the steam and the change in internal energy per expansion stroke are also calculated. A question remains about calculating the work done in an isobaric process for the piston.
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

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?

The exponent is 1.135

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

= 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.

## 1. What is a steam piston and how does it work?

A steam piston is a device used in steam engines to convert the energy of pressurized steam into mechanical work. The piston moves back and forth within a cylinder, pushing a rod that is connected to a crankshaft, which then turns the wheels of the engine.

## 2. What is the connection between steam piston volume and work length?

The volume of the steam piston directly affects the length of the work it can perform. As the volume of the piston increases, it can displace more steam and therefore produce more work. Similarly, a smaller piston will produce less work due to its smaller volume.

## 3. How is work calculated in a steam piston system?

The work in a steam piston system is calculated by multiplying the force applied by the piston by the distance it moves. This can be represented by the equation W = F x d, where W is work, F is force, and d is distance.

## 4. How does the steam pressure affect the work produced by a steam piston?

The steam pressure is a crucial factor in determining the work produced by a steam piston. Higher pressure steam will produce more force on the piston, resulting in more work being performed. On the other hand, lower steam pressure will result in less force and therefore less work.

## 5. Can the volume of a steam piston be changed to increase work output?

Yes, the volume of a steam piston can be changed by adjusting the size of the cylinder or the stroke length of the piston. However, changing these parameters will also affect other factors such as steam pressure and efficiency, so careful calculations and adjustments must be made to achieve the desired increase in work output.

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