1. Understanding Thermodynamic State and Properties
Before applying the First Law of Thermodynamics: Closed & Isolated Systems Explained with Examples to analyze systems, you must understand properties and how they define a system's state.
What is a State?
The state of a system is its condition, defined entirely by its properties. There are two main categories:
- Geometric State: Defined by geometric properties like length, width, height, and roughness.
- Thermodynamic State: Defined by thermodynamic properties like temperature, pressure, density, mass, and internal energy.
What is a Property?
A property is a characteristic of a system that can be evaluated at any given instant (e.g., pressure P, volume V, internal energy U).
Key Distinction: Properties are path-independent (their change depends only on the initial and final states). In contrast, work and heat transfer are not properties; they are energy interactions that cross a system's boundary and cause changes in properties.
- Example: For a stationary closed piston-cylinder system (no change in kinetic/potential energy), the Understanding the First Law of Thermodynamics: Energy Conversion Explained states: [\delta Q - \delta W = dU] Here, U (internal energy) is a property, but Q (heat) and W (work) are not.
2. The Concept of Equilibrium in Thermodynamics
For a system’s state to be accurately defined, it must be in thermodynamic equilibrium. This means that no spontaneous changes occur within the system.
Mechanical Equilibrium (Driven by Pressure)
Thought Experiment: Two different gases in a cylinder separated by a frictionless piston that is initially pinned. The piston allows no heat transfer and no mass flow. When the pin is removed:
- The piston will move in the direction of decreasing pressure.
- The motion stops only when the pressures on both sides are equal ((P_1 = P_2)).
- Result: Mechanical equilibrium is achieved. The system stops changing because the forces (force = pressure × area) on the piston are balanced.
- Key Property: The property associated with mechanical equilibrium is pressure. Temperatures and densities need not be equal.
Thermal Equilibrium (Driven by Temperature)
Thought Experiment: Using the same cylinder, but with a piston that allows heat transfer but no mass flow. The piston is kept pinned (fixed volume). Initially, the gases have different temperatures. A thermal barrier is removed:
- Heat flows from the higher-temperature gas to the lower-temperature gas.
- The system stops changing only when the temperatures on both sides are equal ((T_1 = T_2)).
- Result: Thermal equilibrium is achieved. Temperature differences, not energy levels, drive heat transfer.
- Key Property: The property associated with thermal equilibrium is temperature.
This distinction between mechanical and thermal equilibrium helps clarify how different properties control different types of change, a core theme in Understanding Thermodynamics: A Comprehensive Overview.
Phase Equilibrium
- This involves the balance between different phases (e.g., liquid water and water vapor). The textbook covers this in detail.
Thermodynamic Equilibrium
This is the overarching condition. A system is in thermodynamic equilibrium when all relevant equilibrium conditions are satisfied simultaneously:
- Mechanical equilibrium: (Equal pressure)
- Thermal equilibrium: (Equal temperature)
- Chemical/Phase equilibrium: (No net change in composition or phase)
When a system is in thermodynamic equilibrium with its surroundings, it has the same pressure and temperature as the surroundings.
3. The Zeroth Law of Thermodynamics (Foundation of Temperature Measurement)
The Zeroth Law provides the logical basis for temperature measurement:
If two bodies are in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other.
Practical Implication: It confirms that temperature is the sole driver of thermal equilibrium, not energy content, scale, or pressure. The concept of entropy is also critical here, as it explains another fundamental direction of change, as explored in Understanding Entropy: The Connection Between States and Thermodynamics.
- Example: A small hot stone (40°C) tossed into a large cold lake (20°C). Despite the lake having vastly more total energy, heat flows from the stone to the lake until both reach the same temperature. The temperature difference, not energy difference, dictates the direction of heat flow.
Key Takeaway: This law reinforces that thermal equilibrium is governed only by temperature, allowing us to build reliable thermometers. For a broader view of how these concepts interconnect, refer to Complete Thermodynamics & Thermochemistry Concepts Explained.
okay so we've had a chance to look at a lot of different things now one of the first things we looked at was the fact
that the fundamental measure of energy is work we use that basic definition of work to
define what work looked like in some certain systems then we looked at the different
forms of energy and we actually formed statements of the first law of thermodynamics for an isolated system
where no mass or energy can cross the boundary or we've also looked at the the first law
of thermodynamics for a closed system in which mass can't cross the boundary but
energy in the forms of heat or work can cross the boundaries um what we kind of left off
at is the fact that for us to be able to utilize the first law of thermodynamics to study a system
we have to understand more about properties of the systems so what we're going to do now is we're going to go
down this path of trying to understand a little more about about thermodynamic properties or
about properties in general and there's a lot of little pieces that we have to that we have to work our way
through before it's going to become clear um what what the properties of a system
are so the first thing we have to look at is state and equilibrium in order for us to
define properties we have to understand what is the state
that something is in and whether it's in equilibrium or not so let's start with state the state of
something is its condition defined by properties and so just as as two simple examples
we can look at the geometric state and the thermodynamic state of a system the geometric state of a system can be
defined by for instance the length the width the height maybe the roughness and other
things like that and but you get the idea it has to do with geometric properties
of the system the thermodynamic state of a system is defined by other types of properties
things like the temperature things like the pressure the
density the mass etc and we're going to build on this list another one we've already talked
about which we should put in the list is the internal energy which is related to the temperature but these are all
thermodynamic properties of system that are different from the geometric state so we've got we can
define a geometric state in terms of that and just think about you know how would
you describe something uh if if you were describing it somebody in terms of you know
shape length width height and so forth that would be the geometric condition if you were defining the thermodynamic
state to somebody or describing it to them you wouldn't use things like length with
height you'd be defining in terms of temperature pressure and so forth so that's the distinction between the two
now what is a property so let's look at this very basic system again piston cylinder arrangement it's got a
substance inside and the amount of the substance stays we can do an amount of work we can add an
amount of heat or vice versa we already have defined the the amount of work required to compress such a
substance it's minus pdb now in this case by this definition the pressure and the volume are both
properties if we look at the first law of thermodynamics for this basic closed
system the sum of these two things because i'm showing them both going in
the sum of a small amount of work and a small amount of heat will result in a small change in energy
and if we just consider that this system is stationary meaning that it's not moving around as
we squish it and its position relative to a datum isn't changing
then the change in energy is going to be completely captured by the change in internal energy
because there's no change in kinetic no change in potential in this statement u is a property
so now we've got p is a property v is a property u is a property but it's very important to understand
that the amount of work and the amount of heat transfer are not
properties these are things that are done to a system through the boundaries of the system and
they result in changes in the properties but themselves they're not properties so coming back to this notion of
properties we actually need property values in order to be able to apply the first law of thermodynamics
to thermodynamic systems and also the conservation of mass and eventually the second law of
thermodynamics so properties is is something that we have to be very clear to define we have to be able
eventually to be able to define the condition in terms of properties of any system
that's comprised of you know solid liquid gas or combinations of phases in any condition such that we can apply
the first law of thermodynamics to such systems and this is the path we're going to take
let's continue our discussion about properties by looking at the notion of equilibrium
now there's a couple of different forms of equilibrium and i'm going to go through them carefully
step by step by doing some really simple experiments i want you to really think during these
experiments so let's first talk about this concept of mechanical equilibrium so let's take a situation where we have
a frictionless piston separating two gases so i've just drawn this very basic um chamber and this chamber
has a piston the piston is pinned as i've indicated here the piston is initially pinned
uh separating two different gases that's the easiest way to think about it the volumes are different
the temperatures and pressures can be different at the initial state it doesn't matter but they're two different
gases this piston admits no heat transfer and it admits no mass flow that's what
this m with the little dot means this mass flux okay so we can show here that
none of that is allowed okay no heat transfer no mass flux what we're going to do in this
experiment is simply unpin the piston and then observe the changes in the system because the system
is going to come to rest at some equilibrium and it's going to depend on the
properties of the system so the experiment is unpin the piston
and make some observations so definitely the properties of these systems is going to change
the piston is going to move and the piston is going to move in the direction of decreasing pressure
now if you remember from the work the way that pressure acts on a surface is it acts over an
area to apply a force in this case the area of the piston is the same on both sides
so it's this pressure is acting over the same area as this pressure so as soon as the
pressures become the same then the force that this pressure is applying to this side is going to be
equal to the force that this this pressure is applying to this side and the piston is going to come to rest
because the forces are in balance now this could mean that this temperature suppose that the piston
moves in this direction so if we just think about the gas law this temperature could go down
this density could go down um this temperature could go up and this density could go up but they don't
necessarily become equal because they have nothing to do with the motion of the piston
the motion of the piston is driven entirely by the differential pressures across the two gases
and the fact that the gases are different means that they don't have to have the same temperature and density
for a given pressure so i'm going to note here the piston will eventually
come to a position of equilibrium and we'll call this mechanical equilibrium and this happens when p1 equals p2
regardless of what the two temperatures are regardless of what the densities or even the volumes are
the whole system is is driven to stop when the forces are balanced across the piston so
for mechanical equilibrium we just make the final note that the property associated with mechanical equilibrium
is pressure okay the next type of equilibrium we're going to look at is called thermal
equilibrium so we're going to take exactly the same chamber that we had in the first
instance we're going to replace the piston with a different type of piston but we're going to return it to the
original position so that we're starting out with exactly the same thermodynamic properties on side one and
side two in this case the uh the piston that we've replaced the old one with
is going to allow heat transfer through it but not mass flux not m dot only heat uh in this
experiment we're going to keep the piston pinned okay so we're not allowing the piston to
move which means we're not allowing the volume of this side
and this side to change in time they're fixed at their original positions the properties are different at the
original at the at the starting point in time and when we start the experiment just
imagine that we're going to pull a membrane out of the piston that all of a sudden admits heat transfer from one
side to the other so in this case what we'll observe is that the system is going to
keep it's going to change but it's going to stop changing it's going to come to a state where it doesn't change anymore
as soon as the temperatures are equal so in this case it has nothing to do with pressure in the last case
it was the pressure forces that had to come into balance in this case it doesn't matter because
the piston is pinned in this case because it's a heat transfer the system will stop
when the temperatures are equal because it's temperature differences that drive heat transfer so heat is
going to move from the side of the highest temperature to the lowest temperature
and that can be in either direction but they're going to stop changing when t1 equals t2
so uh in analogy to the last system of mechanical equilibrium the property associated with thermal
equilibrium this one's easy enough to remember is temperature
so now we have two different kinds of equilibria mechanical equilibria associated with pressure and thermal
equilibrium associated with temperature all right so there are other forms of
equilibrium and one of the other ones that i'm going to i'm going to send you to the textbook
to look up is called phase equilibrium so this would be something like if you know air was absorbing water
vapor or something like that i'll i'll get you to the text to read up on that one it's not one that we're going to
talk about very much in this course the other probably most important form of equilibrium is called
thermodynamic equilibrium and thermodynamic equilibrium means that all equilibria prevail that are
associated with energy so generally speaking when we say that a system is in thermal
thermodynamic equilibrium with its surroundings it means it has the same pressure as its surroundings
and it also has the same temperature as its surroundings now there's an important statement that
deals with equilibrium and it's called the zeroth law of thermodynamics so it almost looks like
we've jumped the gun we've already introduced the first law of thermodynamics the reason we do that is
because you've been talking about the first law of thermodynamics probably in some form
since grade 10 or 11 physics the zeroth law of thermodynamics is is a statement about thermal equilibrium so
very specifically we say if two bodies are in thermal equilibrium with a third body
then they're also in thermal equilibrium with each other so basically what it means is that if
two bodies have the same temperature as a third body then all three of them have the same
temperature and they're all in thermal equilibrium with one another seems like a very simple statement it's
actually a statement that tries to reinforce the fact that it's temperature that drives
thermal equilibrium it's not the level of energy it's not the pressure or anything else about the
system it's the temperature of the media so let's think about some really simple examples where you might
you know think about thermal equilibrium if you took for instance a you consider a lake which has got you
know hundreds of thousands of joules of energy in it
and you take a small stone which has very few joules of energy and let's just suppose that the stone
was sitting in the sun so the lake is at 20 degrees celsius and the stone is at
40 degrees celsius and if you toss it into the lake even though the lake has orders of
magnitude more energy than that stone the energy is still going to move from the stone to the lake
until the system is in thermal equilibrium because the temperature of the stone is higher than that of the
lake and thermal equilibrium is driven by the change in temperature
not the difference in energy okay so this this is another really important concept
and when you think of this law i want you to think about the fact that scale doesn't matter we're not talking
about the volume the mass the energy level all we're talking about
is thermal equilibrium and thermal equilibrium is driven by temperature by nothing else except temperature
A thermodynamic property (like pressure, volume, or internal energy) is a characteristic that can be evaluated at any given instant and depends only on the system's state, not the path taken to reach it. In contrast, heat and work are not properties; they are energy interactions that cross a system's boundary and cause changes in properties. For example, in the first law equation δQ - δW = dU, internal energy (U) is a property, while heat (Q) and work (W) are not.
Mechanical equilibrium is achieved when pressures on both sides of a movable boundary (like a piston) are equal (P₁ = P₂), driven by pressure differences. This condition stops any motion due to unbalanced forces. Thermal equilibrium, on the other hand, is achieved when temperatures are equal (T₁ = T₂), driven by temperature differences that cause heat transfer. These two equilibria are independent: a system can be in mechanical equilibrium without being in thermal equilibrium, and vice versa.
For a system to be in thermodynamic equilibrium, all relevant equilibrium conditions must be satisfied simultaneously: mechanical equilibrium (equal pressure throughout), thermal equilibrium (equal temperature throughout), and chemical/phase equilibrium (no net change in composition or phase). When a system is in thermodynamic equilibrium with its surroundings, it has the same pressure and temperature as the surroundings, and no spontaneous changes occur.
The Zeroth Law states: 'If two bodies are in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other.' This law provides the logical foundation for temperature measurement, confirming that temperature alone drives thermal equilibrium. It allows us to build reliable thermometers because a thermometer (the third body) can be used to indirectly compare the temperatures of two other bodies without direct contact, based on their thermal equilibrium with the thermometer.
Heat transfer is driven solely by temperature differences, not by total energy content. The stone at 40°C has a higher temperature than the lake at 20°C, so heat flows from the stone to the lake until they reach thermal equilibrium (equal temperature). The lake's vast total energy is irrelevant because temperature, not energy magnitude, dictates the direction and driving force for heat transfer. This principle is reinforced by the Zeroth Law.
Pressure is the key property for mechanical equilibrium because it directly relates to force (force = pressure × area). In a piston-cylinder system, differences in pressure create unbalanced forces, causing motion. Equilibrium is reached only when pressures equalize, stopping all motion. Temperature is the key property for thermal equilibrium because it determines the direction of spontaneous heat flow. A temperature difference causes heat to transfer from higher to lower temperature until equality is reached, regardless of other properties like density or pressure.
No. A system in thermodynamic equilibrium experiences no spontaneous changes. During heat transfer or work interactions, the system is not in equilibrium because properties like temperature or pressure are changing. Thermodynamic equilibrium is the condition when all relevant equilibrium conditions (mechanical, thermal, chemical/phase) are satisfied simultaneously, meaning no net heat, work, or mass transfer occurs. However, idealized processes can be modeled as quasi-equilibrium (slow enough that the system remains nearly in equilibrium at each step).
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