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### Entropy

What’s wrong with these events?

Introduction

We’ve all spent enough time in this universe to know that things don’t work this way… but how do we explain it?

©1965, James Frankfort & The Curtis Publishing Co.

Entropy

- Here are some things we observe:
- Two gases diffuse into each other and become evenly mixed
- Solids dissolve in liquids until they are evenly scattered
- When a hot object touches a cold one, thermal energy becomes spread among all the particles evenly.

- In all cases, matter and energy become more dispersedspontaneously.

Entropy is a measure of the amount of dispersal or scattering of matter and energy.

Entropy (S)

Clausius chose the word "entropy" because the meaning, from Greek, en+tropein, translated is “transformed content“.

Introduced in 1865 by Rudolph Clausius

Clausius observed that heat cannot flow spontaneously from a material at lower temperature to a material at higher temperature. He also noted that any differences in temperature, pressure, and chemical potential tend to even out in a physical system that is isolated from the outside world.

Entropy is a measure of how much this evening-out process has progressed.

Additionally, Clausius observed that whenever energy is moved or converted, a small amount of energy is incrementally dissipated (Example: frictional losses in mechanical systems).

Entropy (S)

Historically, the concept of entropy evolved in order to explain why some processes are spontaneous and others are not; systems tend to progress in the direction of increasing entropy.

For isolated systems, entropy never decreases. This fact has several important consequences in science:

- it prohibits "perpetual motion" machines
- it suggests an arrow of time

Entropy Applied

Lesser Entropy

Greater Entropy

Organized

Separated

Orderly

Disorganized

Mixed

Random

Increasing

Increasing

Increasing

Increasing

How does the entropy of a system change for each of the following processes?

(a) Condensing water vapor

Randomness decreases increases

Entropy decreases increases

(b) Forming sucrose crystals from a supersaturated solution

Randomness decreases increases

Entropy decreases increases

(c) Heating hydrogen gas from 600C to 800C

Randomness decreases increases

Entropy decreases increases

(d) Subliming dry ice

Randomness decreases increases

Entropy decreases increases

S

nS0(reactants)

S

nS0(products)

=

Entropy Changes in the System (DSsys)

The standard entropy of reaction ( ) is the entropy change for a reaction carried out at 1 atm and 25°C.

For our purposes in Chem-B, entropy is determined this way:

Where q is the flow of heat in or out of a reaction, T is the constant Kelvin temperature, and mol is the amount of matter gaining or losing the heat.

The entropy of a perfect crystalline substance is zero at the absolute zero of temperature.

Entropy Review

- Entropy, S:Measure of dispersal or scattering of energy.
- Can be measured with a calorimeter. Assumes in a perfect crystal at absolute zero, no disorder and S = 0.
- If temperature change is very small, can calculate entropy change, DS = q/T (heat absorbed / T at which change occurs)
- Sum of DS can give total entropy at any desired temperature.
- In general, the final state is more probable than the initial one if:
- energy can be dispersed over a greater number of atoms and molecules (hot cold)
- the atoms and molecules can be more disordered (dissolving, diffusion of gas)

S

nS0(reactants)

S

nS0(products)

=

Example Problem 1What is the standard entropy change for the following reaction at 25°C?

197.9

205

213.6

DS = (-) means that entropy is DECREASING… matter and energy are more organized by this reaction.

The negative DS IS predictable in this reaction.

This reaction is going from 3 moles of gas to 2 moles of gas. When any homogeneous reaction reduces the number of particles, entropy will decrease.

What is the sign of the entropy change for the following reaction?

2 Zn (s) + O2 (g) 2 ZnO (s)

Entropy Changes in the System (DSsys)

When gases are produced (or consumed)

- If a reaction produces more gas molecules than it consumes, DS0 > 0.
- If the total number of gas molecules diminishes, DS0 < 0.
- If there is no net change in the total number of gas molecules, then DS0 may be positive or negative BUT DS0 will be a small number.

The total number of gas molecules goes down, DS is negative.

Entropy Examples (positive DS)

- Boiling water
- Melting ice
- Preparing solutions
- CaCO3 (s) CaO (s) + CO2 (g)

Entropy Examples (negative DS)

- Molecules of gas collecting
- Liquid converting to solid at room temp
- Ag+ (aq) + Cl-(aq) AgCl (s) precipitate forming
- 2 CO (g) + O2 (g) 2 CO2 (g) fewer moles of gas

Entropy Generalizations

- Sgas > S liquid > Ssolid
- Entropies of more complex molecules are larger than those of simpler molecules (Spropane > Sethane>Smethane)
- Entropies of ionic solids are higher when attraction between ions are weaker.
- Entropy usually increases when a pure liquid or solid dissolves in a solvent.
- Entropy increases when a dissolved gas escapes from a solution

Review Laws of Thermodynamics

- First law: Total energy of the universe is a constant.
- Second law: Total entropy of the universe is always increasing.
- Third law: Entropy of a pure, perfectly formed crystalline substance at absolute zero = 0.

Entropy Changes in the Surroundings (DSsurr)

Endothermic Process

DSsurr < 0

Exothermic Process

DSsurr > 0

Second Law of Thermodynamics

In a system, a process that occurs will tend to increase the total entropy of the universe.

Thus, while a system can go through some physical process that decreases its own entropy, the entropy of the universe (which includes the system and its surroundings) must increase overall.

The second law of thermodynamics is an axiom of thermodynamics concerning heat, entropy, and the direction in which thermodynamic processes can occur.

Spontaneous process:

DSuniv = DSsys + DSsurr > 0

Equilibrium process:

DSuniv = DSsys + DSsurr = 0

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