How to calculate work done using a graph

[Apple4ever]

Can someone please tell me how do i calculate work done in 4 process of engine cycles using a graph?

i drew the p-v graph of an gasoline engine cycle now i don't know how to calculate work done. is it by calculating the area inside or how?

no need of formulas...just using the graph..

WORK DONE USING A GRAPH !

 

[Doc Al]

is it by calculating the area inside or how?

Yes, the work done per cycle equals the area enclosed by the PV diagram. Read this: http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heaeng.html#c2"

 

[Apple4ever]

now graphically means do i need to just count the Squares in the closed area or is there any formula to use to find it?

 

[HallsofIvy]

How are you given the graph? Just a picture or are you given a formula? If all you have is a picture, the "counting squares is all you can do. If you are given a formula you can integrate over the area or perhaps integrate around the boundary and use Green's Theorem.

 

[Apple4ever]

Thanks hallsofIvy

Just a picture. now becaususe it's a p-v diagram. i got 31 full squares. i didnt count the half squares which are halfed because of the curve. do i need to count them all as well?

and if it's 31 then what is the unit do i have to use for the answer?

 

[timmay]

You should count them all. You could try scanning the image into Photoshop or similar, calibrating the scale of the squares to pixels and then measuring the area. Or you could use a planimeter - that's typically how you would measure it from an indicator diagram from an engine.

As for units, you know that you're looking for the area of a pressure-volume plot. Thus the units of your area should be the same as the units of pressure multiplied by the units of volume. In an MLT system (mass, length, time) your units should be equivalent to:

$$ML^{2}T^{-2}$$

or in other words, equivalent to a force times a length, which gives you work.