Homework help: work done on gas (Basic thermodynamics)

In summary, the conversation discusses finding the work done on a gas from point R to point P in a cycle of changes. The solution is found by applying the second law for the whole process and adding the area under the curve RP to the area enclosed by the closed path of the cycle. The conversation also mentions the importance of considering whether work is done by the gas or on the gas in determining the sign of the work value.
  • #1
msaleh87
8
0

Homework Statement



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

35a4p5f.png


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

vx0uti.png


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
 
Last edited:
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  • #2
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.
 
  • #3
I think I have found the solution
It is not by counting squares
 
  • #4
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.
 
  • #5
msaleh87 said:
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)
 
  • #6
msaleh87 said:
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.
 
  • #7
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
 
  • #8
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"
 

1. What is work done on gas in basic thermodynamics?

Work done on gas in basic thermodynamics is the measure of energy transfer that occurs when a gas undergoes a change in volume. It is represented by the symbol W and is typically measured in joules (J).

2. How is work done on gas calculated?

The work done on gas is calculated by multiplying the force applied to the gas by the distance over which the force is applied. This can be represented by the equation W = F x d, where W is work, F is force, and d is distance.

3. What is the difference between positive and negative work done on gas?

Positive work done on gas occurs when the gas expands, and the force applied to the gas is in the same direction as the displacement. This results in an increase in the gas's energy. Negative work done on gas occurs when the gas is compressed, and the force applied to the gas is opposite to the displacement. This results in a decrease in the gas's energy.

4. Can work done on gas be negative?

Yes, work done on gas can be negative. As mentioned before, negative work occurs when the gas is compressed, and the force applied to the gas is opposite to the displacement.

5. How does work done on gas relate to the first law of thermodynamics?

The first law of thermodynamics states that energy is conserved, and it cannot be created or destroyed, only transferred. Work done on gas is a form of energy transfer, and it can be used to change the internal energy of the gas, which is a key concept in the first law of thermodynamics.

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