# Can I reverse the PdV integral for work?

• Hercuflea
In summary, the conversation discusses using the equation W = ∫PdV to solve for unknown variables, such as final volume and work, when given known values for pressure and molecular mass. The possibility of reversing the equation into the form W = ∫V dP is also mentioned, but it is ultimately determined that integration by parts is necessary for a solution.
Hercuflea

## Homework Statement

I have a problem where I know P1, P2, V1, and molecular mass. I do not know total mass, final volume, temperature 1 or temperature 2, or the work. I also know that P = 40V^2 + 20

Can I reverse the W = ∫PdV equation into the form W = ∫V dP? Because I could just solve the equation for V = sqrt(P/40 - 1/2) and integrate that. Can I do this?

W = ∫PdV

## The Attempt at a Solution

Qdot - Wdot = mdot ((u2 + v^2/2 + gz2) - (u1 + v^2/2 +gz1))
no heat transfer, constant mass, no change in altitude, no velocity. The system is being compressed.

Hercuflea said:
Can I reverse the W = ∫PdV equation into the form W = ∫V dP? .
Not quite. Integration by parts: ##\int_a^by.dx + \int_{y(a)}^{y(b)}x.dy = [xy]_{x=a}^{x=b}##

## 1. Can I reverse the PdV integral for work?

Yes, the PdV integral can be reversed to calculate work. This is known as the "reversible process" and it follows 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.

## 2. How can the PdV integral be reversed for work calculation?

To reverse the PdV integral for work calculation, one must have knowledge of the change in volume (ΔV) and the pressure (P) of the system. The work can then be calculated using the formula W = -PΔV.

## 3. Is the PdV integral the only way to calculate work?

No, the PdV integral is not the only way to calculate work. Other methods such as the force-distance method and the force-time method can also be used to calculate work.

## 4. What is the significance of the PdV integral in thermodynamics?

The PdV integral is significant in thermodynamics because it helps in understanding the relationship between pressure, volume, and work in a thermodynamic system. It is also used to calculate the work done by or on a system in a reversible process.

## 5. Can the PdV integral be used in all thermodynamic processes?

No, the PdV integral can only be used in reversible thermodynamic processes. In irreversible processes, the work done cannot be calculated using the PdV integral. Other methods such as the force-distance method must be used.

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