The First Law of Thermodynamics

Happy New Week.

The week's topics: UPDATED!!
First Law of Thermodynamics:
- the first law as it relates to the universe;
- revision of heat, work, the thermodynamic potentials (U, H, A, G); and
- the 1st Law and its application to Open Systems

"Thermodynamics is a branch of physics which deals with the energy and work of a system.
Thermodynamics deals only with the large scale response of a system which we can observe and measure in experiments. Small scale gas interactions are described by the kinetic theory of gases.
There are three principal laws of thermodynamics which lead to the definition of thermodynamic properties which help us to understand and predict the operation of a physical system." (NASA).

“The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes.” (All energy in the universe is accounted for). “The laws of thermodynamics are special laws upon which the other [natural] laws depend” (Physical Geo.) It states that:

Q = ΔU + W; or:
ΔU = Q - PΔV

Any change in the internal energy of a particular system is the same as the heat ADDED to the system.
Excluding the work done BY the system.

Heat… work… internal energy? Enthalpy… Gibbs… Helmholtz??? (making sense of it all!)
“We all have a basic understanding of work in general, but scientists have a more precise definition.
For scientists, work is the product of a force acting through a distance;

W = F * s

“When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done by a gas at constant pressure is: P(delta)V (diagram unavailable)

For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is: W = (integral)pv

Work done by a system decreases the internal energy of the system, as indicated in the First Law of Thermodynamics. System work is a major focus in the discussion of heat engines.” (HyperPhysics).

“For a gas, the heat transfer is related to a change in temperature. The temperature, pressure, and volume of the gas determine the state of the gas. Heating a gas changes the state of the gas. But the state of a gas can be changed in a wide variety of ways. (Work done on a gas also changes the state of the gas). The amount of work that a gas can do depends on both the initial and final states and on the process used to make the change. In the same way, the amount of heat transferred in changing the state of a gas also depends on the initial and final states and the exact process used to change the state. Different processes result in different amounts of heat transfer and work. The effects of both heat flow and work are combined in the First Law of Thermodynamics.

There are some thermodynamic processes in which there is no heat transfer. Engineers call this type of a process an adiabatic process and there are simple equations which relate the pressure and temperature of a gas for an adiabatic process.”

Internal Energy
“The internal energy is just a form of energy like the potential energy of an object at some height above the earth, or the kinetic energy of an object in motion.

In the same way that potential energy can be converted to kinetic energy while conserving the total energy of the system, the internal energy of a thermodynamic system can be converted to [other forms of] energy. Like potential energy, the internal energy can be stored in the system. However, heat and work cannot be stored or conserved independently since they depend on the process (the path which leads to the final state of the system).
***NOTE: if you’re wondering WHY they depend on the process, un-squeeze ya face; a good, uncomplicated answer has been included at the end of this post).

“The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But if the process changes the volume, as in a chemical reaction which produces a gaseous product, then work must be done to produce the change in volume. For a constant pressure process the work you must do to produce a volume change ΔV is PΔV. Then the term PV can be interpreted as the work you must do to "create room" for the system if you presume it started at zero volume.” (HyperPhysics).

If a system is fully insulated from the outside environment, it is possible to have a change of state in which no heat is transferred into the system. The implementation of the first law of thermodynamics for gases introduces another useful state variable called the enthalpy.” (NASA)

H = U + PV
“Enthalpy is a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables. It is somewhat parallel to the first law of thermodynamics for a constant pressure system.

It is a useful quantity for tracking chemical reactions. If as a result of an exothermic reaction some energy is released to a system, it has to show up in some measurable form in terms of the state variables. An increase in the enthalpy H = U + PV might be associated with an increase in internal energy which could be measured by calorimetry, or with work done by the system, or a combination of the two.”

Gibbs Free Energy:
“G is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process.

When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy ΔG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible transformation of the system from the same initial state to the same final state.

Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature. As such, it is a convenient criterion of spontaneity for processes with constant pressure and temperature.” (Wikipedia)

Helmholtz Free Energy:
“Helmholtz free energy is a thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume. For such a system, the negative of the difference in the Helmholtz energy is equal to the maximum amount of work extractable from a thermodynamic process in which temperature and volume are held constant.
Under these conditions, it is minimized at equilibrium.

The Helmholtz free energy was developed by Hermann von Helmholtz and is usually denoted by the letter A (from the German “Arbeit” or work), or the letter F . The IUPAC recommends the letter A as well as the use of name Helmholtz energy. In physics, the letter F is usually used to denote the Helmholtz energy, which is often referred to as the Helmholtz function or simply “free energy”.

While Gibbs free energy is most commonly used as a measure of thermodynamic potential, especially in the field of chemistry, the isobaric restriction on that quantity is inconvenient for some applications. For example, in explosives research, Helmholtz free energy is often used since explosive reactions by their nature induce pressure changes. It is also frequently used to define so-called fundamental equations of state in accurate correlations of thermodynamic properties of pure substances.” (Wikipedia)

I’ll look into the derivations of A, G, H et al, but not this week. (PS: I don’t know why blogger has been misbehaving lately).

Special thanks to these fantastic sites:

“The state of a gas is determined by the values of certain measurable properties like the pressure, temperature, and volume which the gas occupies. The values of these variables and the state of the gas can be changed… To change the state of [a] gas from State 1 to State 2, we must change the conditions in the jar, either by:

-heating the gas, or

-physically changing the volume by moving a piston, or

-by changing the pressure by adding or removing weights from [a] piston.

In some of these changes, we do work on, or have work done by the gas, in other changes we add, or remove heat. Thermodynamics helps us determine the amount of work and the amount of heat necessary to change the state of the gas… So we might expect that the amount of work done on, or by a gas could be different depending on exactly how the state is changed. [We could decrease] the pressure and allow the volume to adjust according to Boyle's law with no heat addition. We could [also] move from State 1 to State 2 by holding the pressure constant and increasing the volume by heating the gas using Charles' law… Using either process we change the state of the gas from State 1 to State 2.
But the work for the constant pressure process is greater than the work for the curved line process.

The work done by a gas not only depends on the initial and final states of the gas but also on the process used to change the state. Different processes can produce the same state, but produce different amounts of work.” (I think she’s got it! Lol Plenty thanks NASA!)

The 1st Law and Its Application to Open Systems

First let's revise 3 definitions:

Open System: matter (mass) and energy can cross the boundary into (or out of) the system.

Steady Flow System: where mass in/out equals mass flow in/out
Parameters like Pressure, Mass, Temperature will remain constant with time.

Unsteady Flow System: where mass flow in/out does not equal mass flow in/out
Pressure, Temperature, Mass, etcetera will change with time.

According to some course materials I've read, both steady and unsteady flow situations are present in real systems.
Examples of Steady Flow Systems include: hair dryers, room air heaters, gas turbine compressors, rotary vane compressors.

Good. Now because of the mass continuously entering/leaving the (Open) Systems, 3 forms of energy are transfered:

- Kinetic Energy
- Potential Energy
- "the energy required to 'force' mass into/out of the system against the system's (and surrounding's) pressure" (Ther103)

Work per kg = Pressure x specific volume (in or out) = pv
For mass m, energy = mpv

And with these 3 forms of energy, we will derive the Steady Flow Energy Equation (SFEE):

As the internal energy changes, so do KE, PE and pv energies.Because of work and heat transfer.

For mass m entering and leaving the system:

change in KE = 1/2m(v2^2 - v1^2)
change in PE = mg(h2 - h1)
change in PV = m(p2v2 - p1v1)
Change in U = m(u2 - u1)

Qm + Wm = m[1/2(v2^2 - v1^2) + g(h2 - h1) + (p2v2 - p1v1) + (u2 - u1)]
Divide through by time to obtain rates of energy transfer and mass flow, rearrange:

Q* + W* = m*[1/2(v2^2 - v1^2) + g(h2 - h1) + (p2v2 + u2) - (p1v1 + u1)]
(where Q*, W* and m* are rates of heat work and mass transfer respectively)

A fluid will always have a temperaure and pressure at entry and exit so we combine the last two terms to obtain
the composite property called enthalpy, H = pv + U and re-write the equation as:

Q* + W* = m* (delta)[1/2v^2 + gh + H)

Q* + W* = m*[1/2(v2^2 - v1^2) + g(h2 - h1) + (H2 - H1)]

This, is the Steady Flow Energy Equation.

This can be further simplified to Q* + W* = m*(H2 - H1) because most gases considered in Thermodynamics are low density fluids whose inlet and outlet velocities are often similar (Ther103).
The above equation is called the simplified steady flow energy equation (SSFEE).

However, in Fluid Dynamics which considers liquids which are high density fluids, the SFEE can be simplified to

W* = m* (delta)[1/2mv^2 + gh + pv] because its internal energy does not change considerably (is that really so?)

For further reading:


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