More Discussion of the The 1st Law of Thermodynamics

1st Law of Thermodynamics: Q = Ē + W This form is valid for macroscopic processes in which A, A' are interacting with each other. Now, consider infinitesimal changes in system A’s mean energy dĒ, resulting from interaction with A'.

The 1st Law of Thermodynamics Differential Form of The 1st Law of Thermodynamics Let system A’s mean energy undergo an infinitesimal change dĒ as a result of its interaction with A'. In this process, the infinitesimal amount of heat absorbed by A due to interaction with A' is written as đQ & the infinitesimal amount of work done is written as đW. So, the Differential Form of the 1st Law of Thermodynamics has the form: đQ = dĒ + đW

Differential Form of the 1st Law đQ = dĒ + đW đQ & đW are special symbols which signify that The heat absorbed & the work done are NOT exact differentials! More detailed discussion follows!

Differential Form of the 1st Law: Meaning of Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW đQ & đW are symbols indicating that the heat absorbed & the work done are NOT exact differentials. That is, they are NOT differentials in the rigorous math sense. This is a contrast to dĒ, which is an exact differential. Note: For a process in which system A starts out in state 1 & ends up in state 2, It makes no sense to write: It makes no sense to talk about “the heat of or in a system”! . dQ = Q2 – Q1 (1)

Differential Form of the 1st Law: Meaning of Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW đQ & đW are symbols indicating that the heat absorbed & the work done are NOT exact differentials. That is, they are NOT differentials in the rigorous math sense. This is a contrast to dĒ, which is an exact differential. Note: For a process in which system A starts out in state 1 & ends up in state 2, It makes no sense to write: It makes no sense to talk about “the heat of or in a system”! . dQ = Q2 – Q1 (1)

Differential Form of the 1st Law: It makes no sense to write: Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW It makes no sense to write: l (1) would (incorrectly!) imply the existence of a “heat function” Q, which depends on system A properties & that this “heat function” is changed when A moves from macrostate 1 to macrostate 2. dQ = Q2 – Q1 (1)

Differential Form of the 1st Law: It makes no sense to write: Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW It makes no sense to write: l (1) would (incorrectly!) imply the existence of a “heat function” Q, which depends on system A properties & that this “heat function” is changed when A moves from macrostate 1 to macrostate 2. dQ = Q2 – Q1 (1)

Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW Similar to the heat exchange discussion, when mechanical work is done & system A starts out in state 1 & ends up in state 2, It makes no sense to write: l It makes no sense to talk about “the work of or in a system”! dW = W2 – W1 (2)

Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW Similar to the heat exchange discussion, when mechanical work is done & system A starts out in state 1 & ends up in state 2, It makes no sense to write: l It makes no sense to talk about “the work of or in a system”! dW = W2 – W1 (2)

Differential Form of the 1st Law: It makes no sense to write: Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW It makes no sense to write: l (2) would (incorrectly!) imply the existence of a “work function” W, which depends on system A properties & that this “heat function” is changed when A moves from macrostate 1 to macrostate 2. dW = W2 – W1 (2)

Differential Form of the 1st Law: It makes no sense to write: Meaning of the Symbols đQ & đW Differential Form of the 1st Law: đQ = dĒ + đW It makes no sense to write: l (2) would (incorrectly!) imply the existence of a “work function” W, which depends on system A properties & that this “heat function” is changed when A moves from macrostate 1 to macrostate 2. dW = W2 – W1 (2)

For Macroscopic Processes: The 1st Law of Thermodynamics: Summary For Macroscopic Processes: Q = Ē + W Q

Processes & the System Path Q = Ē + W Q Some Terminology: Processes & the System Path Process: A system change from an initial state to a final state. Path: The total of all intermediate steps between the initial state and the final state in a change of state.

Terminology: Types of Processes Q = Ē + W Q Terminology: Types of Processes Isobaric:  Carried out at constant pressure: p1 = p2. Isochoric:  Carried out at constant volume:V1 = V2. Isothermal:  Carried out at constant temperature: T1 = T2.

Terminology: Types of Processes Q = Ē + W Q Terminology: Types of Processes Adiabatic:  Carried out with no heat exchange: Q = 0. Cyclic:  Carried out with Initial State = Final State.

The Laws of Thermodynamics: Spontaneous & Non-Spontaneous Processes A brief, somewhat philosophical preview of some of the Ch. 3 topics: Spontaneous Processes

The Laws of Thermodynamics: Spontaneous & Non-Spontaneous Processes A brief, somewhat philosophical preview of some of the Ch. 3 topics: Spontaneous Processes Spontaneous Processes are those that will naturally occur in the absence of external driving forces.

The Laws of Thermodynamics & Spontaneous & Non-Spontaneous Processes A brief, somewhat philosophical preview of some of the Ch. 3 topics: Spontaneous Processes Spontaneous Processes are those that will naturally occur in the absence of external driving forces. Of course, such processes must obey The 1st Law of Thermodynamics (Total Energy Conservation) Example: A ball rolls off a table & falls to the floor.

Non-Spontaneous Processes Non-Spontaneous Processes are those that are the reverse of spontaneous processes.

Non-Spontaneous Processes Non-Spontaneous Processes are those that are the reverse of spontaneous processes. This does not mean that non-spontaneous processes don’t happen! They just don’t happen by themselves, but they need an outside influence (force) to take place.

The 1st Law of Thermodynamics Non-Spontaneous Processes Non-Spontaneous Processes are those that are the reverse of spontaneous processes. This does not mean that non-spontaneous processes don’t happen! They just don’t happen by themselves, but they need an outside influence (force) to take place. Such processes must obey The 1st Law of Thermodynamics (Total Energy Conservation)

The 1st Law of Thermodynamics Non-Spontaneous Processes must obey The 1st Law of Thermodynamics (Total Energy Conservation)

The 1st Law of Thermodynamics Non-Spontaneous Processes must obey The 1st Law of Thermodynamics (Total Energy Conservation) The 1st Law is a necessary condition, but its not a sufficient condition for them to take place.

The 1st Law of Thermodynamics The 2nd Law of Thermodynamics Non-Spontaneous Processes must obey The 1st Law of Thermodynamics (Total Energy Conservation) The 1st Law is a necessary condition, but its not a sufficient condition for them to take place. As we’ll see in Ch. 3, to take place, they must also obey The 2nd Law of Thermodynamics (Increasing Entropy)