Homework help: work done on gas (Basic thermodynamics)

[msaleh87]

Homework Statement

A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in the following figure:

Some energy changes during the cycle PQRP are shown in the following figure

Complete the Figure

Homework Equations

Find the work done on gas from R to P

The Attempt at a Solution

I know the work is the are under the curve from R to P
But how to find it
I approximated the curve to a straight line
but I am not sure

Thanks

 

[rock.freak667]

Just find the area of one square and then just count the number squares under the curve.

Which is the simplest way to get an approximate answer. Otherwise you'd need to integrate and whatnot.

 

[msaleh87]

I think I have found the solution
It is not by counting squares

 

[technician]

Have you taken the work done to be the area between the curve and the left hand axis (VOLUME)? This is what it should be !
This graoh has been drawn with V on the vertical axis and P on the horizontal axis. It is usually drawn the other way round... makes a difference to the area you work out.

 

[rock.freak667]

I think I have found the solution
It is not by counting squares

Alternatively you could apply the first law for a cycle which is ∑W = ∑Q (if I remember correctly)

 

[Redbelly98]

I think I have found the solution
It is not by counting squares

That's good. If you share what you found, and how you found it, I can tell you if you're correct. Otherwise, you're on your own.

 

[msaleh87]

ok

firstly note that the axis are reversed "X axis is pressure and Y axis is volume"

the problem is in the last row in the table
how to find the work "the area" under the curved path RP

Appluing the second law but for the whole process:
ΔU=W+Q

here ΔU=o for the whole process
Q= -600+720+480 "for the whole process"
now W= 600

so this is the area enclosed by the closed path "because we applied the 2nd law to the whole process"

now adding the are under PQ to this area, we get the area under the curve RP

 

[Redbelly98]

Looks good, that's the method I was thinking of as well. I'll just add that you want to think about: is work done by the gas, or is work done on the gas? That will affect whether you report a positive or negative value for the problem as given: "Find the work done on gas from R to P"