THERMODYNAMICS

Department of Physics, Faculty of ScienceJazan University, KSA

Part-5

222 PHYS

1st Law

What does the 2nd Law tell us?

Entropy and Temperature, 2nd and 3rd Laws of Thermodynamics

Part-5

(a) “All naturally occurring processes proceed in one direction only. Such spontaneous one-way processes are “irreversible”.

In reversible process, the system and environment will return to their original conditions.

Reversible process

Irreversible processes

Reversible: dissolution of a salt into water, reaction of O2 and H2 to form water, phase changes like freezing or boiling of water

Irreversible: hydrocarbon combustion like the burning of wood or oil, radioactive decay

Processes that are usually idealized as reversible include:•Frictionless movement•Restrained compression or expansion•Energy transfer as heat due to infinitesimal temperature non-uniformity•Electric current flow through a zero resistance•Restrained chemical reaction•Mixing of two samples of the same substance at the same state.

Processes that are irreversible include:•Movement with friction•Unrestrained expansion•Energy transfer as heat due to large temperature non uniformities•Electric current flow through a non zero resistance•Spontaneous chemical reaction•Mixing of matter of different composition or state.

More examples

Physical properties of matter are categorized as either Intensive or Extensive:

•Intensive - Properties that do not depend on the amount of the matter present.•Color•Odor•Luster - How shiny a substance is.•Malleability - The ability of a substance to be beaten into thin sheets.•Ductility - The ability of a substance to be drawn into thin wires.•Conductivity - The ability of a substance to allow the flow of energy or electricity.•Hardness - How easily a substance can be scratched.•Melting/Freezing Point.•Boiling Point.•Density.

•Extensive - Properties that do depend on the amount of matter present.

•Mass - A measurement of the amount of matter in a object (grams).•Weight - A measurement of the gravitational force of attraction of the earth acting on an object.•Volume - A measurement of the amount of space a substance occupies.•Length•Entropy

The second law of thermodynamics introduces the notion of entropy (S), which is a measure of system disorder (messiness)

Note: U is the quantity of a system’s energy, S is the quality of a system’s energy.

The 2nd law of thermodynamics

The 2nd Law can be stated that: heat flows spontaneously from a hot object to a cold object (spontaneously means without the assistance of external work)

Direction of a Process

• The 2nd Law helps determine the preferred direction of a process

• A reversible process is one which can change state and then return to the original state

• This is an idealized condit ion • ( al l real processes are irreversible)

The 2nd law of thermodynamics

0≥dS

Entropy is a physical quantity that controls the direction of irreversible processes.

It is a property of the state of a system; like T, P, V, U.

Entropy principle: “If an irreversible process occurs in a closed system, the entropy of that system always increases; it never decreases.”

Entropy (S )

Another statement of the second law of thermodynamics:

(The total entropy of an isolated system never decreases).

Entropy is a measure of the disorder of a system. This gives us yet another statement of the second law:

Natural processes tend to move toward a state of greater disorder.

Entropy is an extensive thermodynamic property. In other words, the entropy of a complex system is the sum of the entropies of its parts

– The greater the number of possible arrangements, the greater the entropy of a system, i.e., there is a large positional probability.

– The positional probability or the entropy increases as a solid changes from a liquid or as a liquid changes to a gas

Entropy

Ex. Choose the substance with the higher positional entropy:

– CO2(solid) or CO2(gas)?

– N2(gas) at 1 atm and 25oC or N2(gas) at .010 atm and 25oC?

Ssolid < Sliquid < Sgas

Entropy of the System

Is greater in: Gases than solids. Larger volumes of gases than smaller volumes. Larger number of gas molecules than smaller number of

gas molecules.

Example: The second law of thermodynamics leads us to conclude that (A) the total energy of the universe is constant. (B) disorder in the universe is increasing with the passage of time. (C) it is theoretically possible to convert heat into work with 100% efficiency. (D) the average temperature of the universe is increasing with the passage of time.

In fig. below, it can be shown that the gas and the reservoir form a closed system. The entropy change of this closed system is found to be zero: .

The second law of thermodynamics and Entropy

When the systems for the irreversible processes are closed, the corresponding . 0>∆S

0=∆ totS

insulating

Thermal reservoir

gas

T

|Q|Sgas =∆

T

|Q|Sreservoir −=∆ } 0, =∆ closedtotS

For expansion process

Probability of Disorder

• Entropy is defined as a measure of disorder.

• A system (such as a room) is in a state of high entropy when its degree of disorder is high.

• As the order within a system increases, its entropy decreases.

•Is there a higher probability your room will be messy or neat as time goes on?

Entropy change for reversible processes

The definition of entropy change for a reversible process: (reversible)

∫=∆f

i T

dQS

Here dQ is the increment of heat energy that is transferred into (or out) of the closed system at temperature T.

If the process is isothermal,

if the entropy of that system increases and if, the entropy of that system constant

T

QS =∆

0>Q 0>∆S

0 0Q S= ⇔ ∆ =

Divided by T, we obtain

dU dQ dW= +

PdVdW −=

vdU nC dT=v v

nRTdQ nC dT PdV nC dT dV

V= + = +

v

dQ dT dVnC nR

T T V= +

Entropy as a state property

{

Integrate between an arbitrary initial state i and an final state f :

f f fi V

i i

T VdQS nC ln nR ln

T T V∫∆ = = +

from the first law

What’s the entropy change for ideal gases?

P=nRT/V

Only related to initial and final states

Example5-1

A vessel containing 1.8kg of water is placed on a hot plate. Both the water and hot plate being initially at . The temperature of the hot plate is raised very slowly to at which point the water begins to boil. Find of the water during this process?

c100S∆

c20

f f

i i

T T fT T

i

TdQ dTS mc mcln 1818 J/K

T T TΔ ∫ ∫= = = =

mcdTdQ =Solution:

c= 4186 J kg¯1 K¯1

Processes can be discussed profitably using the entropy concept.For a reversible process:

∫=−=∆B

A

AB T

QSSS

δ

• If the reversible process is isothermal:

STQT

QQ

TSSS

B

A

AB ∆=⇒==−=∆ ∫δ1

S increases if the system absorbs heat, otherwise S decreases

00 =∆⇒==−=∆ ∫ ST

QSSS

B

A

AB

δ

Reversible isothermal processes are isentropic but in irreversible ones the entropy may change

• If the reversible process is adiabatic:

Example: A heat source at 800 K loses 2000 kJ of heat to a sink at (a) 500 K and (b) 750 K. Determine which heat transfer process is more irreversible.

(a) For the heat transfer process to a sink at 500 K:

(b) Similarly, for process at 750 K:

Process (b) is less irreversible since it involves a smaller T difference (smaller irreversibility).

∫=B

A

TdSQIn a finite process: (depends on the trajectory)

In a cycle:

=−==∫ WTdSQ work done by the system in the cycle

Q

heat absorbed by system

Q

∆S = 0

Entropy and the performance of engines

• A heat engine is a device that extracts energy from its environment in the form of heat and does useful work.

• At the heart of every engine is a working substance (gas). • For an engine to do work on a sustained basis, the working substance must operate in a cycle.

This will be discussed in details in next module

Energy is conservedo FIRST LAW OF THERMODYNAMICSo Examples: Engines (Internal -> Mechanical)

Friction (Mechanical -> Internal) All processes must increase entropy

o SECOND LAW OF THERMODYNAMICSo Entropy is measure of disordero Engines can not be 100% efficient

In short