Work Done by Gas PV Diagram

In summary, the problem is to find the work done by each path in the given PV diagram. The solution is to use the equation W=P(delta)V for paths a-b and c-d, where W represents work, P is pressure, and V is volume. For paths a-c and b-d, the work done is 0. The question is what is the work done by the gas for path a-d, and the answer is found by calculating the area under the curve, which in this case is a trapezoid. This means the work done is equal to deltaP times deltaV, and since P is no longer constant, it must be integrated as well.
  • #1
Malicious
16
0
Problem.
http://img294.imageshack.us/img294/8068/pvdiagram2fo.gif
Find Work done by each path.

My Solution.
a-b, c-d >> W=P(delta)V
a-c, b-d >> W=0

My Question.
What is the work done by the gas (path a-d)?

My Thoughts.
There is a change in both pressure and volume. However, the equation to find the work in this situation is "W=P(delta)V". There is no (delta)P.
 
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  • #2
could anyone help him?I'm kinda interested in the answer to this as well!
 
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  • #3
Are you familiar with integration? The answer is always found by calculating the area under the curve, which is exactly what you did for all the other ones. In this case, the area is a trapezoid
 
  • #4
so the work done from a to d is W = deltaP * deltaV
very good, P is no longer constant so integrate that as well
as if it was that simple
 
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What is work done by gas on a PV diagram?

Work done by gas on a PV diagram is a measure of the energy transferred to or from a gas as it expands or contracts at a constant pressure. It is represented by the area under the curve on a PV diagram.

How is work done by gas calculated on a PV diagram?

The work done by gas on a PV diagram is calculated by multiplying the pressure by the change in volume. This can be represented mathematically as W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume.

What is the significance of the sign of work done by gas on a PV diagram?

The sign of work done by gas on a PV diagram tells us whether the gas is doing work (positive sign) or work is being done on the gas (negative sign). A positive sign indicates that the gas is expanding and doing work on its surroundings, while a negative sign indicates that the gas is being compressed and work is being done on it by its surroundings.

What is the relationship between work done by gas and heat on a PV diagram?

Work done by gas and heat are both forms of energy transfer, but they are not directly related on a PV diagram. Work done by gas is represented by the area under the curve, while heat is represented by the change in internal energy. The two may be related through the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Can work done by gas be negative on a PV diagram?

Yes, work done by gas can be negative on a PV diagram if the gas is being compressed and work is being done on it by its surroundings. In this case, the area under the curve will be below the x-axis, indicating a negative value for work done.

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