The 1st Law of Thermodynamic states that energy is conserved in any process, but it does not tell us whether the process will occur in the first place or not
- This is an issue because we intuitively know that there are processes that obey the conservation law but will never happen
- We therefore need another fundamental law to tell us whether an event will occur
The conservation law doesn’t tell us why there is preference given to a particular direction of changes
- In other words, why things change in a particular manner as time moves forward?
- Put it another way, what distinguishes from time going forward and time going backward?
The total energy of an isolated system is constant, but the energy is parceled out in different ways
- The direction of spontaneous change is related to the distribution of energy
- In order to understand the tendency for the dispersion of energy, we must familiarize ourselves with the concept of entropy
The Second Law of Thermodynamics can be summarized as such :
- This event will continue to occur until its occurence no longer stabilizes the universe. At this point, a state of high stability is attained and equilibrium is established
We can interpret the second law as a tendency to reach equilibrium
- Once equilibrium is disturbed, the return to equilibrium is inevitable
- The pathway to equilibrium always involves the occurance of an event that increases the stability of the universe
All processes can therefore fall under one of two categories
- A natural process is one that will increase the stability of the universe when it takes place
- An unnatural process is one that will decrease the stability of the universe when it takes place
We have established that whether an event can happen is determined by its ability to bring about stability to the universe, but that is hardly quantitative
- If there are multiple potential natural processes, only one will take place
- We therefore need to devise a way to let us determine which one of those is more favorable
In order to quantiy stability, we must define a new state variable, entropy ( )
- The more stable a state is, the higher its entropy
Entropy must be a state quantity because the stability of a state does not depend on how it came to be
- In other words, entropy is an inherent property just like temperature, pressure, volume e.t.c.
We can relate predict whether a process can happen by determining the change in stability in the initial and final state
- A process is natural if it will cause the universe to go from a state of low stability to a state of high stability
- A process is in equilibrium if the initial and final state of the universe has the same stability
- A process will not take place if it will cause the universe to go from a state of high stability to a state of low stability
- We can describe these statements mathematically since the difference in stability between two states is given by
We can therefore describe the second law mathematically
- A process can only take place if the change in entropy satisfies the inequality
- Unless the it is in equilibrium, the entropy of the universe always increases
Although we are able to quantify stability, it is hardly convenient to predict whether a process is favorable by determining the change in entropy of the entire universe every time
- In thermodynamics, we are primarily interested in the system, so it makes sense to break down the entropy of the entire universe into a sum of entropy
The consequence of splitting the total change in entropy is that a natural process can take place with a local decrease in entropy
- In other words, as long as the total change in entropy is positive, an event can occur even when either the system or the surrounding experience a decrease in entropy
The change in entropy of the universe for a reversible process is 0
- A process is reversible if it can proceed without departure from equilibrium
- As established before, the change in entropy of the universe is zero when it is in a state of equilibrium. Hence, the change in entropy of the universe must also be zero for the entire reversible process
The change in entropy of an irreversible process is positive
- An irreversible process does not proceed through a series of equilibrium states
- Once equilibrium is disturbed, the return to equilibrium is inevitable, and it always involves an increase in entropy
The fact that a reversible process and an irreversible process results in a differentchange in entropy change of the universe may seem paradoxical since we have established that entropy is a state quantity
- The key to this is understanding that both the reversible and the irreversible pathway brings the system to the same final state, but they do not bring the universe to the same final state
- A reversible process is one that occurs without changing the surrounding permanantly, while an irreversible process changes the surrounding permanantly
- As a result, the final state of the surrounding, hence, the final state of the universe, is different for a reversible and an irreversible process
The thermodynamic definition of entropy concentrates on the change in entropy, dS, that occurs as a result of a physical or chemical change ( or process in general )
- The definition of entropy instructs us to find the energy supplied as heat for a reversible path between the stated initial and final states regardless of the actual manner in which the process takes place
Entropy can be thought of as the degree of dispersal of thermal energy within the system. The definition is motivated by the idea that a change in the extent to which energy is dispersed depends on how much energy is transferred as heat
- Heat stimulates random motion of particles, thus increases the entropy
- Work stimulates organized and uniform motion of particles, so the entropy is unchanged
Entropy is the flow of heat that results in the system losing capacity to do work
- We can interpret entropy as the amount of energy that is wasted ( not able to do work, but dissipated as heat )
It is essentially a threshold for how significantly you can increase the dispersion of particle energy in a system by supplying heat into the system
- The higher the resultant entropy, the more influential the heat flow was, and the less heat you needed to impart into the system to get its energy distribution to a certain amount of dispersiveness
Reversible heat flow is greater than irreversible heat flow
- We have proven the inequality before
- We can rearrange it to
- From the 1st Law, we know that , and we also know that the change in internal energy does not depend on the reversibility of the process
- If we put all the variables to the same sides, we will get
- We know that the left side of the equation is greater than or equal to 0, so we can create a new inequality
- Put in another way
Since reversible heat is related to entropy, we can create an inequality for entropy as well
- If we divide the inequality concerning the heat flow by the temperature at which it is transferred, we will get
We can recognize that the left side of the inequality is equivalent to the change in entropy, so we can substitute it for that
The equality is applicable to reversible process, and the inequality is applicable to irreversible process
- For irreversible, spontaneous processes
- In order to satisfy the inequality, q must be irreversible heat flow
- For reversible processes, or at equilibrium
- In order to satisfy the equality, q must be reversible heat flow
- For nonspontaneous processes
- In order to satisfy the inequality, q must be negative, meaning that heat is flowing out of the system, which is only possible if work is done on the system
If we now consider an isolated system instead, no heat flow is allowed ( đq = 0 ), therefore đq divided by T is also equal to zero. We can therefore revise the above statements
- If dS > 0, then the process is irreversible and spontaneous
- If dS = 0, the entropy is constant, then the process is reversible and is at equilibrium
- If dS < 0, the process is not allowed
Thus, we can conclude that, for an isolated system, any spontaneous change will tend to produce states of higher entropy until the entropy reaches a maximum. At this point, the system will be in equilibrium and the entropy will remain constant at its maximum value
- The universe, being an isolated system, will have its entropy keep increasing until it eventually reaches a maximum. Hence, we can use the total entropy of the entire universe as an indicator of spontaneity