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MindMap Gallery Second Law of Heat, Entropy and Carnot Cycle

Second Law of Heat, Entropy and Carnot Cycle

The second law of heat, entropy and Carnot cycle, spontaneous process: whether it is spontaneous or not depends on the state of the initial and final states, whether it is reversible or not depends on the driving force of the process (reversible: the driving force is infinitely small; irreversible: the driving force is large).

Edited at 2023-07-30 10:23:46

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Second Law of Heat, Entropy and Carnot Cycle

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Outline

hot two

spontaneous process

Features

ability to do work

irreversibility

Have definite directions and limits

Whether it is spontaneous or not depends on the state of the initial and final states, and whether it is reversible or not depends on the driving force of the process (reversible: the driving force is infinitely small; irreversible: the driving force is large)

Second law of heat

Clausius

It is impossible for heat to be transferred from a low-temperature object to a high-temperature object without causing other changes.

Kelvin

It is impossible to take heat from a single heat source and turn it completely into work without other changes (second perpetual motion machine ❌)

Carnot cycle

Heat engine and second perpetual motion machine

Heat engine: low temperature heat source✔️

The second perpetual motion machine: low temperature heat source ❌

Carnot heat engine: The working material absorbs heat Q2 from the high-temperature heat source (T2), part of it does work W, and part of it releases heat Q1 to the low-temperature heat source (T1).

Heat engine efficiency: η

formula:

inference

For any heat engine between the same high-temperature/low-temperature heat source, all Carnot (reversible) heat engines have maximum and equal efficiencies.

The efficiency of the Carnot heat engine is only related to the temperatures of the two heat sources and has nothing to do with the working medium.

The greater the temperature difference between the two heat sources, the greater the heat engine efficiency; conversely, the smaller the

entropy

Features

state function

It only depends on the initial and final states of the process

breadth property

Additive

Unit: J/K

Physical meaning: measure of the number of microstates of a system

S=k·lnΩ

S gas>S liquid>S solid

S high temperature>S low temperature

S low pressure>S high pressure

ΔSmix>0

The sum of the heat and temperature quotients of any reversible cycle is 0

The heat temperature quotient of a reversible process = the change in the entropy function✅, that is, the entropy change✅, not the entropy❌

Clausius inequality

The sum of the heat-temperature quotients of an irreversible process is less than the entropy change between the initial and final states of the process. Numerically, the sum of the heat-temperature quotients of a reversible process is 🟰0

Formula: Reversible Process irreversible process

entropy increase

Adiabatic system (Q=0)

ΔS>0

Adiabatic irreversibility, entropy increases

ΔS=0

Adiabatic reversibility, entropy remains unchanged

It can only be judged whether it is reversible✅, but not whether it is spontaneous❌

Isolated system (Wf=0, Q=0)/the environment is only the atmosphere

formula:

ΔSiso>0

Irreversible🟰Spontaneous

ΔSiso=0

Reversible🟰Balance/reach limit

ΔSiso<0

Not spontaneous🟰impossible

Can determine process direction and limits✅

Carnot cycle

formula

entropy change

chemical reaction entropy change

Standard reaction entropy change 🟰Standard entropy of products ➖Standard entropy of reactants

Conditions: Each substance is in standard state

formula:

use:

Kirchhoff's formula:

Three laws of heat

At 0K, the entropy of a complete crystal of any pure substance is 🟰0

A complete crystal has only one arrangement

0K cannot be reached by finite steps

Specified entropy: The entropy value relative to the zero point specified by the three laws of heat

Standard molar entropy: the specified entropy value of 1 mol of a substance in the standard state

Helmholtz energy (F)

F🟰Ｕ-TS

State function, ΔF is only related to the initial and final states, unit: J

Work function, reservoir of work

formula:

Meaning: When the closed system is waiting for T to be reversible, the Helmholtz energy decreases🟰The reversible system does the maximum work

Gibbs free energy

G🟰Ｈ-TS

State function, ΔG is only related to the initial and final states, unit: J

formula:

In the reversible process of waiting for T and P, the Gibbs energy of the closed system decreases🟰 The maximum non-volume work done by the system

Criteria for the direction and limits of spontaneous processes

Calculation of ΔF and ΔG

thermodynamic function relationship

Basic relations of thermodynamics

Maxwell's relation