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ITK-233Termodinamika Teknik

Kimia I

3 SKS

4 - The Second Law: Entropy

Process Direction

No apparatus can operate in such a way that its only effect (in system & surroundings) is to convert heat absorbed by a system completely into work done by the system

It is impossible by a cyclic process to convert the heat absorbed by a system completely into work done by the system.

No process is possible which consist solely in the transfer of heat from one temperature level to a higher one.

Partial conversion of heat to into work is the basis for nearly all commercial production of power.

Heat Engine

Heat engines produce work from heat in a cyclic process

Essential to all heat-engine cycles are: Absorption of heat into the system at a high

temperature Rejection of heat to surroundings at a lower

temperature Production of work

Conversion of heat to work always accompanied by heat release to surroundings

Heat Engine

CHoutin QQQQW

Thermal efficiency: absorbedheat

outputworknett

H

C

H

CH

H Q

Q1

Q

QQ

Q

W

For to be unity, QC must be zero. No engine has ever been built for which this is true; some heat is always rejected.

Carnot’s Theorem & Carnot Engine

Carnot engine operates between two heat reservoirs

in such a way that all heat absorbed is absorbed at the constant temperature of the hot reservoir

and all heat rejected at the constant temperature of the cold reservoirFor two given heat reservoir, no engine can have a thermal

efficiency higher than that of a Carnot engine.

Carnot Cycle

Step1: A system at TC undergoes a reversible adiabatic process that causes its temperature rise to TH

Step 2: The system maintains contact with the hot reservoir TH, and undergoes a reversible isothermal process during which heat QH is absorbed from the hot reservoir

Step 3: The system undergoes a reversible adiabatic process in the opposite direction of step 1 that brings its temperature back to that of the cold reservoir at TC.Step 4: The system maintains contact with the reservoir at TC, and undergoes

reversible isothermal process in the opposite direction of the step 2 that returns it to its initial state with heat rejection of QC to the cold reservoir

Carnot Engine - Reversibility

Any reversible engine operating between 2 heat reservoirs is a Carnot engine.

An engine operating on a different cycle must necessarily transfer heat across finite temperature difference and therefore cannot be reversible.

Carnot Cycle with an Ideal Gas as Working Fluid

Step1: a - bReversible adiabatic compression until

the temperature rise from TC to TH

Step 2: b – cReversible isothermal expansion to

arbitrary point c with heat absorption of QH

Step 3: c – dReversible adiabatic expansion until the

temperature decrease TC.Step 4: d – a Reversible isothermal compression to the initial state with heat rejection of QC

Entropy

Our analysis showed that or

The equation suggests the existence of a property whose changes are given by the quantities Q/T

When the isotermal steps are infinitesimal, the heat quantities become dQ: or

Thus the quantities dQrev/T sum to zero for the arbitrary cycle, exhibiting the characteristic of a property. We call this property as entropy, S.

0T

Q

T

Q

C

C

H

H C

H

C

H

T

T

Q

Q

0T

dQ

T

dQ

C

C

H

H 0T

dQrev

T

dQdS rev dSTdQrev

There exists a property called entropy S, which is an intrinsic property of a system, functionally related to the measurable coordinates which

characterize the system

Characteristic of Entropy

Entropy owes its existence to the second law, from which it arises in much the same way as internal energy does from the first law.

The change in entropy of any system undergoing a finite reversible process is

When a system undergoes an irreversible process between two states, the entropy change of the system is evaluated to an arbitrary chosen reversible process that accomplishes the same change of state as the actual process. The integration is not carried out for the irreversible path.

T

dQS rev

Characteristic of Entropy

Since entropy is a state function, the entropy changes of the irreversible and reversible processes are identical.

The entropy change of a system caused by the transfer of heat can always be calculated by dQ/T whether the heat transfer is accomplished reversibly or irreversibly.

When a process is irreversible on account of finite differences in other driving forces, such as pressure, the entropy changes is not caused solely by heat transfer, and for its calculations one must devise a reversible means of accomplishing the same change of state.

Calculation of Entropy

For one mole of fluid undergoing a mechanically reversible process in a closed system, using the first law, the defining equation for enthalpy one find:

For an ideal gas:

Although derived for a mechanically reversible process, this equation is a general equation for the calculation of entropy changes, since it relates properties only and independent of process causing the change of state.

T

dPV

T

dH

T

dQdS rev

0

T

T

igp

P

Pln

T

dT

R

C

R

S

0

Example

Calculate ΔS for each step of the cycle shown below. Assume ideal gas with constant Cp.

Problem 5.6

A quantity of an ideal gas, Cp = 7/2 R at 20oC & 1 bar and having a volume of 70 m3 is heated at constant pressure to 25oC by the transfer of heat from a heat reservoir at 40oC. Calculate the heat transfer to the gas, the entropy change of the heat reservoir, the entropy change of the gas, and DStotal.

Problem 5.7

A rigid vessel of 0.05 m3 volume contains an ideal gas, Cv = 5/2 R, at 500 K and 1 bar.

a. If heat in the amount of 12000 J is transferred to the gas, determine its entropy change

b. If the vessel is fitted with a stirrer that is rotated by a shaft so that work on the amount of 12000 J is done on the gas, what is the entropy change of the gas if the process is adiabatic? What is DStotal?

Example 5.3

Methane gas at 550 K & 5 bar undergoes a reversible adiabatic expansion to 1 bar. Assuming methane to be an ideal gas at these conditions, determine its final temperature.

Heat Engine

CHoutin QQQQW

Thermal efficiency: absorbedheat

outputworknett

H

C

H

CH

H Q

Q1

Q

QQ

Q

W

For to be unity, QC must be zero. No engine has ever been built for which this is true; some heat is always rejected.

Mathematical Statement of The Second Law

0Stotal

This mathematical statement of the second law affirms that every process proceeds in such a direction that the total entropy change associated with it is positive.

The limiting value of zero being attained only by a reversible process.

No process is possible for which the total entropy decreases.

Thermodynamic Efficiency

In a process producing work, there is an absolute maximum work attainable which is accomplished by completely reversible process. For irreversible process, Wactual produced < Wideal

In a process requiring work, there is an absolute minimum amount of work required which is accomplished by completely reversible process. For irreversible process, Wractual required > Wideal

t

ideals

WW

idealts WW

Problem 5.12

An ideal gas, Cp = 7/2 R, undergoes a cycle consisting of the following mechanically reversible steps:

a. An adiabatic compression from P1, V1, T1 to P2, V2, T2

b. An isobaric expansion from P2, V2, T2 to P3 = P2, V3, T3

c. An adiabatic expansion from P3, V3, T3 to P4, V4, T4

d. A constant-volume process from P4, V4, T4 to P1, V1 = V4, T1

Sketch this cycle on a PV diagram and determine its thermal efficiency if T1 = 500 K, T2 = 800 K, T3 = 2000 K, and T4 = 1000 K

Problem 5.13

A reversible cycle executed by 1 mol of an ideal gas for which Cp = 5/2 R consist of the following processes:

a. Starting at 600 K & 2 bar, the gas is cooled at constant pressure to 300 K

b. From 300 K & 2 bar, the gas is compressed isothermally to 4 bar

c. The gas returns to its initial state along a path for which the product PT is constant.

What is the thermal efficiency of the cycle?

Example 5.4

A 40-kg steel casting (Cp = 0.5 kJ/(kg.K) at a temperature of 450oC is quenched in 150 kg of oil (Cp = 2.5 kJ/(kg.K) at 25oC. If there are no heat losses, what is the change of entropy of:

a. The castingb. The oilc. Both considered together

Problem 5.11

A piston/cylinder device contains 5 mol of an ideal gas, Cp = 5/2 R, at 20oC & 1 bar. The gas is compressed reversibly and adiabatically to 10 bar, where the piston is locked in position. The cylinder is then brought into thermal contact with a heat reservoir at 20oC, and heat transfer continues until the gas also reaches this temperature. Determine the entropy changes of the gas, the reservoir, and DStotal

Irreversibility

One mole of an ideal gas, Cp = 7/2 R is compressed adiabatically in a piston/cylinder device from 2 bar & 25oC to 7 bar. The process is irreversible and requires 35% more work than a reversible adiabatic compression from the same initial state to the same final pressure. What is the entropy change of the gas?

Classical Lost Work & Process Analysis

The ideal work is the maximum amount of work which can be done by the process by operating reversibly within the system and by transferring heat between the system and the surroundings reversibly.

The lost work:

For processes containing several units, lost-work calculations can be made for each unit and summed to determine the overall value.

actualideallost WWW

QSTW slost

Example 4.7

Steam enters a turbine at 1.5 MPa & 500oC and exhausts at 0.1 MPa. The turbine delivers 85% of the shaft work of a reversible-adiabatic turbine although it is neither reversible nor adiabatic. Heat losses to the surroundings at 20oC are 9 kJ/kg steam.

Determine temperature, entropy change of the steam leaving the turbine, & the lost work

Example 4.8

Assume that 5000 kg/h of oil with a heat capacity of 3.2 kJ/kg.K is to be cooled from 220 to 40oC, using a large quantity of water which can be assumed to be at a constant temperature of 30oC. Determine the lost work in the process and the thermodynamic efficiency of the process.

Example 4.9

Assume that 100 kg of methane gas/h is adiabatically compressed from 0.5 MPa & 300 K to 3.0 MPa & 500 K after which it is cooled isobarically to 300 K by a large amount of water available at 290 K. Determine the efficiency of the compressor.

If the surroundings are assumed to be at 290 K, do a thermodynamic analysis of the process.

Assume ideal gas.Cp = 35.58 J/mol.KCv = 27.27 J/mol.K

8

Steam dengan tekanan 12 bar dan temperatur 200 oC diekpansi satu tahap dalam sebuah turbin sehingga tekanannya menjadi 1,5 bar pada kondisi jenuhnya. Turbin bekerja secara adiabatik dengan efisiensi 85%. Perkirakan (dalam sistem satuan SI):

Kualitas uap keluar turbinKebutuhan uap air agar dihasilkan daya

sebesar 50 MWattKerja ideal, kerja musnah dan perubahan

entropi total, jika temperatur lingkungan 25 oC

Problem 5.8

An ideal gas, Cp = 7/2 R, is heated in a steady-flow heat exchanger from 20oC to 100oC by another stream of the same ideal gas which enters at 180oC. The flow rates of the two streams are the same, and heat losses from the exchanger are negligible.

a. Calculate the molar entropy changes of the two gas streams for both parallel and counter-current flow in the exchanger

b. What is DStotal in each case?

Carnot Cycle

Suatu mesin Carnot menyerap panas sebesar 400 kJ dari sumber panas pada 525 oC dan melepas panas ke penerima panas pada 50 oC. Perkirakan kerja yang dihasilkan, perubahan entropy sumber panas, penerima panas dan total!

2nd law

Satu mol gas ideal dikompresi secara isotermal-ireversibel pada 130 oC dari 3 bar menjadi 6.5 bar dalam sebuah alat silinder berpiston. Kerja yang dibutuhkan untuk kompresi ini 30% lebih besar dari kerja untuk proses reversibelnya. Selama kompresi, sejumlah panas dibuang ke lingkungan yang memiliki temperatur konstan sebesar 25 oC. Hitung perubahan entropi dari gas, penerima panas dan total!

2nd law

Uap jenuh dengan tekanan 5 bar dan temperatur 151,87 oC berada dalam silinder yang volumnya 0,750 m3. Silinder tersebut dilengkapi dengan piston yang dapat bergerak bebas. Uap air tersebut kemudian dikompresi secara reversibel sampai diperoleh uap air yang memiliki tekanan 12 bar dan temperatur 187,99 oC. Selama proses kompresi berlangsung, terjadi pembuangan panas ke lingkungan sejumlah 2000 kJ. Temperatur lingkungan diketahui sebesar 27 oC. Perkirakanlah:a. Prosentase uap air yang mengembunb. Perubahan entalpi dan energi dalam (dalam kJ/kg)

Kerja yang dibutuhkan untuk kompresi tersebut (dalam kJ)

Perubahan entropy uap air, lingkungan dan total

2nd law

Gas nitrogen dengan laju 2 ton/jam mula-mula memiliki temperatur -168 oC dan tekanan 1 Mpa. Gas nitrogen tersebut kemudian dikompresi secara adiabatik dalam sebuah kompresor sehingga temperatur dan tekanannya masing-masing menjadi –63 oC dan 6 MPa. Dari deskripsi proses tersebut:

Dengan mengasumsikan gas nitrogen sebagai gas ideal, perkirakan daya yang dibutuhkan (dalam kWatt), efisiensi mekanik (dalam %) dan perubahan entropi gas nitrogen pada proses kompresi tersebut! Ambil = 1,4.

Dengan menggunakan diagram P-H gas nitrogen terlampir, jawablah kembali pertanyaan soal a!

7

Karbon tetrakhlorida cair sebanyak 5 kg mengalami perubahan secara reversibel pada tekanan konstan sebesar 1 bar dalam sistem tertutup. Akibat perlakuan tersebut, temperatur fluida mengalami perubahan dari 0 oC menjadi 56 oC. Sifat-sifat dari CCl4 cair pada 1 bar dan 0 oC diasumsikan tidak dipengaruhi temperatur: = 1,2 x 10-3 K-1, CP = 0,84 kJ kg-1 K-1, dan = 1,590 kg/m3. Tentukanlah:a. Perubahan entropi dari karbon tetrakhlorida cair b. Temperatur lingkungan pada saat proses perubahan tersebut berlangsung (dalam oC)

Jika proses berlangsung secara ireversibel, perkirakan efisiensi mekanik alat apabila kerja yang mampu dihasilkan sebesar 11,67 kJ!

Berkaitan dengan soal c, hitunglah perubahan entropi total! Apa kesimpulan yang dapat diambil!Ambil nilai temperatur lingkungan sama dengan hasil perhitungan soal b!