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이 병 주 포항공과대학교 신소재공학과 [email protected] Thermodynamics. The First Law. First Law of thermodynamics - Various Forms of Work. 0. Hydrostatic system PdV 1. Surface film SdA 2. Stretched wire FdL 3. Reversible cell εdZ

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이 병 주

포항공과대학교 신소재공학과

[email protected]

Thermodynamics

The First Law


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First Law of thermodynamics - Various Forms of Work

0. Hydrostatic system PdV

1. Surface film SdA

2. Stretched wireFdL

3. Reversible cell εdZ

4. Dielectric slab EdΠ

5. Paramagnetic rod μoHdM


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First Law of thermodynamics - Is Heat an Energy?

▷ Count Rumford (1798): heat produced during boring of cannon was roughly

(Benjamin Thompson) proportional to the work performed during the boring

▷ Humphrey Davy (1799): End of Caloric Theory

← Melting of two blocks of ice by rubbing them in vacuum

▷ Mayer, Helmholtz 등 에너지 보존 법칙의 가능성을 언급

▷ James Joule observed: (1840 ∼)

A direct proportionality existed between the work done and the resultant

temperature rise. The same proportionality existed no matter what means

were employed in the work production

· Rotating a paddle wheel immersed in the water

· A current through a coil immersed in the water

· Compressing a cylinder of gas immersed in the water

· Rubbing together two metal blocks immersed in the water

※ Mechanical equivalent of heat with unit calorie


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First Law of thermodynamics - First Law

  • “The change of a body inside an adiabatic enclosure from a

  • given initial state to a given final state involves the same

  • amount of work by whatever means the process is carried

  • out”

  • It was necessary to define some function which depends only on the

    internal state of a body or system

    – Internal Energy.

  • For adiabatic process: UB – UA = -w

  • Generally: UB – UA = q - w

  • dU = δq - δw

  • : as a state function


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First Law of thermodynamics - Special processes

Absolute value of U is not known: Necessity of Special Paths

1.Constant-Volume Process: ΔU = qv

2. Constant-Pressure Process: ΔH = qp

⇒ concept of heat capacity: ,

,

3. Reversible Adiabatic Process: q = 0

4. Reversible Isothermal Process: ΔU = ΔH = 0

※ Importance of the identification of state functions

→ justification of the analysis of unrealistic reversible processes


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First Law of thermodynamics - Some issues

or dU = Cv dT

or dH = Cp dT

or

or


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First Law of thermodynamics - Special Processes

Reversible Adiabatic Process: q = 0

for ideal gas

= constant

Reversible Isothermal Process: ΔU = ΔH = 0


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First Law of thermodynamics - Numerical Example


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이 병 주

포항공과대학교 신소재공학과

[email protected]

Thermodynamics

The Second Law


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Second Law of thermodynamics - Introduction

Spontaneous (or Natural or Irreversible) Process

▷ mixing of two gases

▷ Equalization of temperature

▷ A + B = C + D : criterion for equilibrium?

Entropy as a measure of the degree of irreversibility

▷ Lewis and Randall’s Consideration: A weight-pulley-heat_reservoir

▷ q/T = △S


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Second Law of thermodynamics - Reversible vs. Irreversible

△S = measurable quantity + un-measurable quantity

= q/T + △Sirr

= qrev/T


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Second Law of thermodynamics - Evaluation of Entropy Change

▷ Reversible Isothermal Compression of an Ideal Gas

▷ Reversible Adiabatic Expansion of an Ideal Gas

Isentropic process: ΔU = -w


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Second Law of thermodynamics - Engines and Referigerators


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▷ Carnot, 1824 - 열기관의 효율은 이를 구성하는 두 온도만의 함수.

(caloric 이론에 의거)

▷ Joule, 1847 - 에너지는 보존되고, 여러 형태가 서로 변환이 가능함을

실험적으로 제시 → Mayer, Helmholtz 등의 에너지보존법칙에 final touch.

▷ Thomson - Carnot와 Joule 사이에 모순이 있음을 지적

▷ Clausius, 1850 - Joule을 인정하면서 Carnot의 원리 증명.

같은 일을 하면서 더 적은 열을 흡수(q2’)하고 방출(q1’)하는 엔진과

정상적인 Heat Pump를 결합, q2 - q2’ = q1 – q1’.

열이 낮은 온도에서 높은 온도로 흐르지 않는다.

따라서 Carnot의 원리는 성립한다.

▷ Thomson, 1851 - Carnot의 원리 증명

열을 흡수해서 모두 일로 바꾸는 것이 불가능

같은 열을 흡수하면서 더 많은 일과(w’) 더 적은 열을 방출(q1’)하는

엔진과 정상적인 Heat Pump를 결합, w’- w = q1 – q1’

열을 100% 일로 바꿀 수는 없다. 따라서, Carnot의 원리는 성립한다.

▷ Thomson, 1852 - 현재 물질 세계에는 역학적 에너지의 낭비를 향한

일반적 경향이 존재한다.

▷ Clausius, 1865 - 우주의 에너지는 일정하다. 우주의 엔트로피는 항상 증가한다.

Second Law of thermodynamics - Historical Background


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Second Law of thermodynamics - Thermodynamic Temperature Scale

  • Concept of Absolute Temperature

  • ▷ The maximum efficiency is independent of the working substance

  • and is a function only of the working temperatures, t1 and t2.

Kelvin Scale (Absolute Thermodynamic Temperature Scale, K)

0K is the temperature of the cold reservoir which makes the efficiency

Of a Carnot cycle equal to unity


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Second Law of thermodynamics - Equivalence of temperature scales

Equivalence of Kelvin Scale and Ideal Gas Temperature Scale

▷Efficiency of Carnot Cycle:

▷ Carnot cycle이 두 개의 reversible isothermal process와 두 개의 reversible

adiabatic process로 이루어졌다고 가정하고 ideal gas temperature scale에

기초하여 효율을 계산하면 (T2-T1)/T2라는 같은 결과나 나온다.


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Second Law of thermodynamics - Entropy as a State Function

For a Carnot Cycle

For an arbitrary Cyclic process which can be broken into a large number of small Carnot cycle.

※로 정의되는 entropy S는 state function이고 adiabatic system에서

감소할 수 없다.


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Second Law of thermodynamics - Entropy and Irreversibility

▷ Processes exhibiting Mechanical Irreversibility

Coming to rest of a rotating or vibrating liquid in contact

with a reservoir

Ideal gas rushing into a vacuum

▷ Processes exhibiting Thermal Irreversibility

Conduction or radiation of heat from hotter to cooler system/reservoir

▷ Processes exhibiting Chemical Irreversibility

Mixing of two dissimilar inert ideal gases

(※ example: k ln Ω, ln x! = x ln x – x )

Freezing of supercooled liquid

(※ example: freezing of supercooled Pb)


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Second Law of thermodynamics - Maximum Work


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Second Law of thermodynamics - Entropy as a Criterion of Equilibrium

※ for an isolated system of constant U and constant V,

(adiabatically contained system of constant volume)

equilibrium is attained when the entropy of the system is maximum.

※ for a closed system which does no work other than work of

volume expansion,

dU = T dS – P dV (valid for reversible process)

U is thus the natural choice of dependent variable for S and V

as the independent variables.

※ for a system of constant entropy and volume, equilibrium is attained

when the internal energy is minimized.


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Second Law of thermodynamics - Condition for Thermodynamic Equilibrium

※ Further development of Classical Thermodynamics results from the fact

that S and V are an inconvenient pair of independent variables.

+ need to include composition variables in any equation of state and

in any criterion of equilibrium

+ need to deal with non P-V work

(e.g., electric work performed by a galvanic cell)

※ Condition for Thermodynamic Equilibrium of a Unary two phase system

The same conclusion is obtained using minimum internal energy criterion.


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Second Law of thermodynamics – Numerical Example


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