Thermodynamics Constant Pressure Process

In summary, the first equation states that the sum of heat and work done is equal to the change in internal energy, while the second equation says that the work done by the system is done by subtracting the heat supplied from the final internal energy minus the work done.
  • #1
raniero
42
0
Hi, I found a derivation for heat transfer in a constant pressure process. It goes as follows:

Q + W = u2 - u1
Q = u2 - u1 + p(v2 - v1)

Since h = u + pv, Then

Q = h2 - h1

The first equation states that the sum of heat and work done is equal to the change in internal energy, I can comprehend up to there. But in the next line the work done is taken to the other side of the equation; both mathematically and physically I cannot understand how the work done (p(v2 - v1)) is still positive.

Mathematically I would say that taking work to the opposite side would make work negative.
Physically I would think that the amount of heat supplied/given off would be equal to the difference of initial and final internal energy minus the work done.

Hope someone could clear this out for me. Thanks
 
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  • #2
The First Law of Thermodynamics states that for a system ΔE = Q-W,
which states that the change in energy of a system equals the heat added to the system minus the work done by the system. If we neglect changes in kinetic energy and potential energy of the system , then this can be written as,
ΔU = Q - W

where W = P(V2 - V1 )

in which case you should have no problem determining that Q = h2-h1 for a constant pressure process.

IF instead you consider the work done on the system by the surroundings as positive and write,
ΔU = Q + W
then the work is done by the system is -P(V2 - V1 ). Notice the minus sign.
Note that for an expansion of the gas, V1 < V2, and for a compression V1 > V2.

Take note that we are looking at the change in energy of the system.
You have to keep in mind of how energy is crossing the state boundary of the system and whether you will consider work W entering the system as positive ( in which case work W leaving the system is negative ), or negative.

Your statement should actually be, bold added,
Q + W = u2 - u1
.
.
The first equation states that the sum of heat ADDED TO THE SYSTEM and work done ON THE SYSTEM is equal to the change in internal energy ...

Or
Q-W = u2-u1
The first equation states that the sum of heat ADDED TO THE SYSTEM and work done BY THE SYSTEM is equal to the change in internal energy ...

Notice the difference.
 
  • #3
I see, thanks for the detailed explanation :)
 

1. What is a constant pressure process in thermodynamics?

A constant pressure process in thermodynamics is a type of thermodynamic process where the pressure of the system remains constant throughout. This means that the system is allowed to exchange heat with its surroundings, but the external pressure remains the same. This type of process is commonly referred to as an isobaric process.

2. How is the thermodynamics constant pressure process represented on a P-V diagram?

On a P-V (pressure-volume) diagram, a constant pressure process is represented by a horizontal line parallel to the x-axis. This indicates that the pressure remains constant while the volume of the system changes.

3. What is the relationship between heat and work in a constant pressure process?

In a constant pressure process, the amount of heat added to the system is equal to the change in enthalpy of the system, which is represented by ΔH. The work done by the system is equal to the product of the pressure and the change in volume, which is represented by W = PΔV. Therefore, the relationship between heat and work in a constant pressure process can be expressed as: ΔH = Q - PΔV.

4. Is the internal energy of a system constant in a constant pressure process?

No, the internal energy of a system is not constant in a constant pressure process. This is because the system is allowed to exchange heat with its surroundings, which can result in a change in the internal energy of the system.

5. What are some real-life examples of constant pressure processes in thermodynamics?

Some real-life examples of constant pressure processes include boiling water in an open pot, where the pressure remains constant at atmospheric pressure while the water boils and changes from liquid to gas. Another example is a car engine, where the combustion of fuel and air occurs at constant pressure, resulting in the expansion of gases and the movement of the pistons.

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