제 8장 비반응 공정의 에너지 수지

제 8장 비반응 공정의 에너지 수지

1절 학습개요

 상태 특성치와 가상 공정경로

 등온하의 압력변화

 온도에 따른 변화

 상변화 조작

 혼합과 용해

2.1절 학습목표

 물성표를 이용하지 않는 에너지 수지 이해

 혼합과 분리시의 에너지 수지 이해

• 공정의 초기상태에서 최종상태로의 가상공정 경로 이해

• 정온하에서의 압력변화에 따른 에너지 변화 이해

• 온도변화에 따른 에너지의 변화 이해

• 상변화시의 에너지 변화 이해

• 습도도의 사용법 이해

2.2절 학습 목적

• After completing this chapter, you should be able to do the following:

– Define both formally (in terms of internal

energies and enthalpies) and in words a high school senior could understand the variables

Cv(T) (heat capacity at constant volume ), Cp(T) (heat capacity at constant pressure), (heat of fusion or heat of melting), (heat of

vaporization), standard heats of fusion and

vaporization, and (heat of solution or heat of mixing).

Hm Δ ˆ Hˆ v

∆ Hs

Δ ˆ

– Calculate and for the following

changes in state of a species, when possible using enthalpies and internal energies, heat capacities, latent heats, and liquid and solid specific gravities tabulated in this text: (a) isothermal changes in pressure. (b) isobaric (constant-pressure) changes in temperature, (c ) isothermal isobaric phase changes, and (d) isothermal isobaric mixing of two or more

species. State when the formulas you use for these calculations are exact, good

approximations, and poor approximations.

∆Uˆ

∆ Hˆ

– Given a reference state (phase, temperature, and pressure) and a process state for a

species, (a) choose a path from the reference state to the process state consisting of a series of isothermal pressure changes, isobaric

temperature changes, and isothermal isobaric phase changes; (b) calculate and for the species at the process state relative to the species at the reference state.

– High school physics and chemistry texts

commonly state that the heat (Q) required to raise the temperature of a mass m of a

substance by an amount is where C_p is defined as the heat capacity of the

substance. Explain why this formula is only an approximation. List the assumptions required to obtain it from the closed system energy

balance

Uˆ Hˆ

∆ T

) (Q −W =∆U +∆E_k +∆E_p

– If your class covers Section 8.3e, evaluate

Using the trapezoidal rule or Simpson’s rule (Appendix A.3) from data for C

at several temperatures between T

and T

. – Estimate the heat capacity of a liquid or

solid species using Kopp’s rule.

Estimate the heat of fusion and heat of vaporization of a species using

correlations in Section 8.4b.

∫

C

⁽ T ⁾ dT

–Given any non-reactive process for which the

required heat transfer Q or heat transfer rate is to be calculated, (a) draw and label the

flowchart, including Q or in the labeling ; (b) carry out a degree-of-freedom analysis ;

(c) write the material and energy balances and other equations you would use to solve for all

requested quantities ; (d) perform the calculations ; and (e) list the assumptions and approximations

built into your calculations.

Q

Q

– Given an adiabatic process or any other

nonreactive process for which the value of Q (closed system) or (open system ) is specified, write material and energy balance equations and solve them simultaneously for requested quantities.

– Define the dry-bulb temperature, wet-bulb temperature, and humid volume of humid air.

Given values of any two of the variables plotted on the psychrometric chart (dry-bulb and wet- bulb temperatures, absolute and the relative

humidity, dew point, humid volume), determine the remaining variable and the specific enthalpy of the humid air. Use the psychrometric chart to carry out material and energy balance

calculations on a heating, cooling,

humidification, or dehumidification process involving air and water at 1 atm.

Q

– Explain the meaning of the apparently contradictory term adiabatic cooling . Explain how spray cooling and

humidification, and spray drying work.

Explain how it is possible to dehumidify air by spraying water into it. Use the

psychrometric chart to carry out material and energy balance calculations on an adiabatic cooling operation involving air and water at 1 atm.

– Explain to a first-year engineering

student why a beaker containing acid

gets hot if you add water to it.

– Use the heat of solution data in Table B.10 and solution heat capacity data to (a) calculate the enthalpy of a hydrochloric acid, or sodium

hydroxide solution of a known composition

(solute mole fraction) relative to the pure solute and water at 25ºC ; (b) calculate the required rate of heat transfer to or form a process in which an aqueous solution of HCl, H₂SO₄, or NaOH is formed, diluted, or combined with

another solution of the same species ; and (c ) calculate the final temperature if an aqueous solution of HCl, H₂SO₄, or NaOH is formed, diluted, or combined with another solution of the same species adiabatically.

– Perform material and energy balance calculations for a process that involves solutions for which enthalpy-

concentration charts are available.

3절 학습내용

1.1a 기준 상태 : 복습

H

U ˆ ˆ ,

H U ˆ , ∆ ˆ

∆

U

U

U ˆ = ˆ − ˆ

∆

있슴.

V P U

H U

U 0

U ˆ

=  → ˆ = ∆ ˆ  → ˆ = ˆ + ˆ

어느 특정 온도에서의 비용과 압력 으로부터 비엔탈피 계산 가능

스팀 도표의 비내부에너지와 비엔탈피값 : -기준 상태(삼중점) 액체 내부에너지 값 = 0

-H₂O(l, 0.01°C,0.00611 bar)→H₂O(v, 400°C, 10.0 bar) : ∆Û=2958 kJ/kg - = 2958+(10 bar)(0.307 mHˆ = Uˆ + PVˆ ³/kg)(10³ L/m³)=3264 kJ/kg

 공정경로 : 초기 상태에서 최종 상태로 가는 하나의 가상적인 연속 단계

공정경로 각 단계의 합 전체 공정에 대한 ex)

∆Hˆ

∑

∆

=

∆ ⁶

1

ˆ ˆ

i

Hi

H

전체 공정에 대해

∆Hˆ

페놀(s, 25℃, 1 atm) 증기 300℃, 3 atm

페놀(s,42.5℃, 1 atm)

페놀(l, 42.5℃, 1 atm)

페놀(l, 181.4℃, 1 atm) 증기 181.4℃, 1 atm 증기 300℃, 1 atm 실제 경로

가

상 공 정 경 로

1.1b 상태 특성값과 가상 공정경로

 상태 특성 값인 : 오직 주어진 상태(온도, 압력, 기-액-고 응집 상태)함수 U ˆˆ, H

Hˆ 1

∆ Hˆ 2

∆

Hˆ

∆

내부에너지와 엔탈피 변화 발생 특정 경로:

- 일정 온도, 응집 상태에서 압력 변화(8.2절) - 일정 압력, 응집 상태에서 온도 변화(8.3절) - 일정 온도, 압력 상태에서 상변화(8.4절) - 일정 온도, 압력 상태에서 (8.5절)

- 두 액체 혼합

- 액상에 기체 용해 - 액상에 고체 용해 - 화학 반응 (9장)

1.1c 에너지 수지 계산 순서

1. 물질 수지 계산 수행.

2. 닫힌 계, 열린 계에 대한 적절한 에너지 수지식 작성: 각 항이 0 이거나 무시 가능한 항들 삭제. (예: 운동에너지, 위치에너지, 샤프트에너지 등) 3. 공정에 나타난 각각 물질마다 기준 상태 선정 (예: 상, 온도, 압력 등 이

용, 물과 같은 도표 이용 가능 물질: 도표 제작에 사용된 상태, 기타 다른 물질: 주입 혹은 배출 상태 선정)

4. 닫힌 계 : 물질 별 초기, 최종질량에 대한 열(column)으로 된 표 작성. 줄 (row)에는 기준 상태를 기준으로한 비내부에너지(혹은 비엔탈피) 작성.

5. 열린 계 : 물질 별 주입, 배출질량에 대한 열(column)으로 된 표 작성. 줄 (row)에는 기준 상태를 기준으로한 비엔탈피 작성.

6. 계산 수행 : 1. 닫힌 계 : 2. 열린 계 :

∑

∑

=

∆

initial

i i final

i

iU n U

n

U ˆ ˆ

∑

∑

=

∆

in

i i out

i

iH n H

n

H  ˆ  ˆ

7. 에너지 수지식에서 생략한 일, 운동에너지, 위치에너지 계산 8. 미지 변수값에 대한 최종 에너지 수지식 계산 : 종종 Q 혹은

-닫힌 계 : ∆U + ∆Ε_k + ∆E_p = Q - W

-열린 계 :

예제 8.1-1 : 다음 쪽

Q

S p

k Δ E Q W

Δ E

Δ H +  +  =  − 

Ex 8.1-1 Energy Balance on a Condenser

Acetone is partially condensed out of a gas stream containing 66.9

mole % acetone vapor and the balance nitrogen. Process specifications and material balance calculations lead to the flowchart shown below.

The process operates at steady state. Calculate the required cooling rate.

Solution

1. Perform required material balance calculations.

2. Write and simplify the energy balance.

3. Choose reference states for acetone and nitrogen.

Table B.8 ⇒ specific enthalpies of N₂ relative to N₂(g, 25℃,1 atm)

No enthalpy data for Ac ⇒

4. Construct an inlet-outlet enthalpy table.

∑

∑

=

∆

=

⇒

≈

∆

≈

∆

=

∆ +

∆ +

∆

=

−

in out

p k

s

p k

s

ˆ ˆ

) 0 ,

0 ,

0 (

i i i

iH n H

n H

Q

E E

W

E E

H W

Q



 















 

현현 현 현현현현 현현현 현 현현현현.

) 5

, 20

, (

ˆ 0 at Ac l C atm

H = ^o

5. Calculate all unknown specific enthalpies.

atm) 1

℃, 65 Ac(v, atm)

5

℃, 20 (l, Ac ˆ for

atm) 5

℃, 20 (l, Ac to relative atm)

1

℃, 65 (v, Ac of enthalpy specific

ˆ1

→

∆

=

= H H

path 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

atm) 1

℃, 65 Ac(v, atm)

1

℃, 56 Ac(v,

atm)

℃,1 56 Ac(l, atm)

1

℃, 20 Ac(l, atm)

5

℃, 20 Ac(l,

1 1

1 1

H H

d c

b a

H H

H H

∆

=

⇒



 →





 →





 →





 →



∆

∆

∆

∆

• Section 8.2 ⇒

The value of for liquid acetone is 0.0734L/mol from the specific gravity of 0.791 given in Table B.1

• Section 8.3 ⇒ , Cp : Table B.2

P V H = ∆

∆ ˆ ˆ

Vˆ

∫

=

∆ ²

1

) ˆ ^T (

T Cp T dT H

3 12 2

8 5

p

5 p

10 76

. 34 10

78 . 12 10

10 . 20 07196

.

℃ 0 mol : kJ

Ac(v)

, 10

18.6 0.123

℃ mol : kJ

Ac(l)

T T

T C

C in is T where T

C ^o

−

−

−

−

× +

×

−

× +

 =



 





⋅

× +

 =



 





⋅

• Section 8.4 ⇒ Table B.1 lists T_bp for acetone as 56.0℃ and as 30.2 kJ/mol.

Proceeding in a similar manner, we obtain the value for )

ˆ (

bp

V T

∆H

kJ/mol 35.7

kJ/mol )

753 . 0 2 . 30 68

. 4 0297 .

0 (

) ( ˆ )

( )

( atm)

5 atm ˆ (1

ˆ ˆ

ˆ ˆ

ˆ ˆ

atm) 1

℃, 65 Ac(v, atm)

1

℃, 56 Ac(v,

atm) 1

℃, 56 Ac(l, atm)

1

℃, 20 Ac(l, atm)

5

℃, 20 Ac(l,

56℃

℃ 20

℃ 65

℃

56 Ac(v)

Ac v Ac(l)

Ac(l)

1 1

1 1

path 1

ˆ ˆ

ˆ ˆ

1 1

1 1

= +

+ +

=

+

∆ + +

−

=

∆ +

∆ +

∆ +

∆

=

∆

=

⇒



 →





 →





 →





 →



∫ ∫

∆

∆

∆

∆

dT Cp

H dT

Cp V

H H

H H

H H

d c

b a

H H

H H

d c

b a

ˆ . , ˆ

ˆ2 H3 and H4

H

6. Calculate .

7. Calculate nonzero work, kinetic energy, and potential energy terms.

8. Solve the energy balance for .

∆H

kJ/s 2320

kJ/s 6)]

(33.1)(1.1 7)

(66.9)(35.

0.10) (33.1)(

) [(63.55)(0 kJ/mol)

0 mol/s)(32.

(3.35

ˆ ˆ

in out

−

=

−

−

− +

+

=

−

=

∆^H

∑

∑

Q

kW 2320

kJ/s

2320 = −

−

=

∆

= H Q 