What is the relationship between work and pressure in a PV graph?

In summary, the sign of work done in a PV graph is positive if there is an increase in volume. This is because for all processes in a gas, the work done is equal to the integral of pressure and volume, which results in a positive value when volume is increasing. The formulas given by the teacher are only valid for isothermal processes in an ideal gas, and the graph shown does not correspond to these formulas. The integral is also equal to the area under the curve, which in both parts of the diagram is increasing.
  • #1
pulkit707
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If in PV graph work goes down and then goes up please tell sign of work done and why?My teacher says no matter what preesure is if volume is increasing then work is positive but w=nRTln(p1/p2) and w=nRTln(v2/v1) also .
 

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  • #2
The graph that you have shown does not correspond to the formulas you have written. Both formulas are valid only for isothermal processes in an ideal gas. For all processes in a gas, the work done is given by

W = ∫ pdV where the limits of integration are from an initial volume to a final volume. If there is an increase in the volume, then the integral is positive, and the work is positive. The integral is equal to the area under the curve, and in both parts of your diagram, the volume is increasing.
 

FAQ: What is the relationship between work and pressure in a PV graph?

1. What is the relationship between work and pressure?

The relationship between work and pressure is direct. This means that as pressure increases, work also increases. Similarly, as pressure decreases, work decreases.

2. How does pressure affect the amount of work done?

Pressure is a measure of the force applied over a certain area. In order to do work, a force must be applied to an object. Therefore, as pressure increases, the force applied also increases, resulting in more work being done.

3. Can work be done without pressure?

Technically, yes. Work can be done without pressure if there is a constant force being applied to an object, regardless of the area over which the force is applied. However, in most cases, pressure is necessary for work to be done.

4. How does pressure affect the amount of force needed to do work?

Pressure and force are directly proportional. This means that as pressure increases, the amount of force needed to do work also increases. In other words, higher pressure requires a greater force to do the same amount of work.

5. Does work always depend on pressure?

No, work can also depend on other factors such as distance, displacement, and the angle of application of the force. However, pressure is a key factor in determining the amount of work that can be done in a given situation.

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