# Thermodynamic Work: Find w P, V, T Not Constants

• thejinx0r
In summary, thermodynamic work is the energy transferred between systems due to changes in volume or pressure. It is calculated using the formula w = -PΔV, where w is work, P is pressure, and ΔV is the change in volume. Thermodynamic work can be negative, and the unit of measurement for it is joules (J) in the International System of Units (SI). The more general formula for calculating work when pressure, volume, and temperature are not constant is w = -∫PdV, which allows for changes in pressure and volume.
thejinx0r
Hi,

How can I find the thermodynamic work from
dw=Pdv

if P, Vand T are not constants?
what if I knew that dp/dv is a constant in this case?

You need to express P as a function of V first. Then you can evaluate the integral,

W = ∫ P dV

The thermodynamic work, w, can be calculated by integrating the equation dw=Pdv over the desired volume range. In this case, since P, V, and T are not constants, the value of P may vary at different volumes. This means that the thermodynamic work will also vary, as it is dependent on the pressure and volume of the system. Therefore, to find the work, you would need to have knowledge of how the pressure changes with volume. If you know that dp/dv is a constant, then you can use this information to solve for the pressure at different volumes and then integrate to find the work. However, if dp/dv is not a constant, then you would need additional information or data to accurately calculate the thermodynamic work.

## 1. What is thermodynamic work?

Thermodynamic work is the amount of energy transferred from one system to another due to a change in volume or pressure. It is a form of energy that is often associated with the movement of matter.

## 2. How is thermodynamic work calculated?

Thermodynamic work can be calculated using the formula w = -PΔV, where w is work, P is pressure, and ΔV is the change in volume. This formula assumes that pressure and volume are constant during the process.

## 3. Can thermodynamic work be negative?

Yes, thermodynamic work can be negative. This occurs when the system does work on its surroundings, resulting in a decrease in its internal energy. For example, when a gas expands against a constant external pressure, the work is negative.

## 4. How do I find thermodynamic work when pressure, volume, and temperature are not constant?

In order to find thermodynamic work when pressure, volume, and temperature are not constant, you need to use the more general formula w = -∫PdV, where the integral is taken over the path of the process on a P-V diagram. This allows for changes in pressure and volume during the process.

## 5. What is the unit of measurement for thermodynamic work?

The unit of measurement for thermodynamic work is joules (J) in the International System of Units (SI). However, other units such as calories (cal) and foot-pounds (ft-lb) are also commonly used.

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