What is Entropy?What is Entropy?Tds Relations andTds Relations and

ΔΔS of Liquids and SolidsS of Liquids and Solids

What is entropy?What is entropy?• Cannot define or explain what it is physically Cannot define or explain what it is physically

to my satisfaction.to my satisfaction.• Doesn’t detract from its usefulness.Doesn’t detract from its usefulness.• Can be viewed as a measure of Can be viewed as a measure of molecular molecular

disorder disorder or or molecular randomness.molecular randomness.– Lowest in solid phase and highest in gas phaseLowest in solid phase and highest in gas phase

– Boltzmann relation: Boltzmann relation: S = k S = k ln ln p.p.• pp is called thermodynamic probability = total number is called thermodynamic probability = total number

of possible microscopic states of a system.of possible microscopic states of a system.

Perfect order →its entropy is zero (Third law of thermo).

Disorganized energy is not much use.Gas molecules have a lot of energy butit is not organized.

Therefore, the gas cannot turn a paddlewheel and produce work.

Raising a weight by a rotatiingshaft does not create anydisorder (entropy) so energy isnot degraded. (no friction)

There is no entropy transferassociated with energy transfer aswork.

Therefore, this work is reversible.

This work, done on a gas, increases the level of disorder(entropy) of the gas, and thus energy is degraded.

so this process is not reversible

Quality of energy transferred decreases because it has less valueat lower temperature.

The increase in entropy of the cold body more than offsets the decrease in entropy of the hot body.

Entropy principles applyto our every day lives.

Efficient people lead low-entropy (highly organized)lives.

They have a place foreverything (maximumuncertainty). A minimum ofenergy to find anything.

The entropy of my office is large.

From an energy balance with substitutions of δQ = TdS andδW = PdV, we get the “Tds” equations:

Both are good for both systems

Can solve for ds and integrate for ideal gases

Entropy Change of Liquids and SolidsEntropy Change of Liquids and Solids

• Can be approximated as incompressible Can be approximated as incompressible substances.substances.– gets rid of the gets rid of the Pdv Pdv part of the first Tds equation.part of the first Tds equation.

• Leaves: Leaves: ds = du/T = CdT/Tds = du/T = CdT/T• Which when integrated gives: Which when integrated gives: ss22 – – ss1 1 = =

CCavavln(ln(TT22/T/T11))• For substances that expand a lot with Temp, For substances that expand a lot with Temp,

must take must take ΔΔvv into account. into account.• Also says that isentropic processes are also Also says that isentropic processes are also

isothermal with incompressible substances.isothermal with incompressible substances.• See Table 6 – 1 page 322.See Table 6 – 1 page 322.