이 병 주 포항공과대학교 신소재공학과 email@example.com. 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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The First Law
0. Hydrostatic system PdV
1. Surface film SdA
2. Stretched wire FdL
3. Reversible cell εdZ
4. Dielectric slab EdΠ
5. Paramagnetic rod μoHdM
▷ 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
internal state of a body or system
– Internal Energy.
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
or dU = Cv dT
or dH = Cp dT
Reversible Adiabatic Process: q ＝ 0
for ideal gas
Reversible Isothermal Process: ΔU ＝ ΔH ＝ 0
The Second Law
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
△S = measurable quantity + un-measurable quantity
= q/T + △Sirr
▷ Reversible Isothermal Compression of an Ideal Gas
▷ Reversible Adiabatic Expansion of an Ideal Gas
Isentropic process: ΔU = -w
(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
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
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.
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.
▷ 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)
※ 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
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.
※ 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.