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Thermodynamics&

Heat transferLecture 04

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Instructor: Dr. Qari Khalid Waheed

Institute of Mechatronics Engineering,

UET Peshawar.

BY: Engr. Muhammad Usman Khan

(MtE-203)

Fall 2015

The 2nd

Law of thermodynamics

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The laws of thermodynamics describe the relationships between thermalenergy, or heat, and other forms of energy, and how energy affectsmatter.

2nd Law states that, in any complete cycle the gross heat supplied plus thenet work input must be greater than zero.Thus for any cycle in which there is a net work output (i.e. W = - ve), heat must

always be rejected.

For any cycle in which heat is supplied at a low temperature and rejectedat high temperature there must always be a positive work input.

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Fig 1: Second Law: Heat Engines (Alternative statement)

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The heat engine

A heat engine is a system which operates continuously and across whoseboundaries flow only heat and work.

2nd Law can also be defined as:It is impossible to extract an amount of heat QH from a hot reservoir and use it all

to do work W . Some amount of heat QC must be exhausted to a cold reservoir.This precludes a perfect heat engine.

Forward heat engine shown in Fig.2, and reverse heat engine shown inFig.3

In both cases the first law applies. i.e.

𝑸 + 𝑾 = 0

Q1 + Q2+ W = 0

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5Fig 2: Forward Heat Engine

Qh +ve

Qc –ve

W –ve

Cyclic efficiency;

Ƞ = – W/ Qh

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Qh –ve

Qc +ve

W +ve

Fig 3: Reverse Heat Engine

Cyclic efficiency;

Ƞ = W/ Qc

Used as

refrigerator

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Entropy

Entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder.

According to the 2nd law of thermodynamics the entropy of an isolated system never decreases; such a system will spontaneously proceed towards thermodynamic equilibrium, the configuration with maximum entropy.

• For a reversible adiabatic process, dQ/T = 0

• While for any other reversible process, dQ/T ≠ 0

ds = dQ/T , for all working substances

The change of entropy is more important than its absolute value.

Integrating the above equation;

s2 - s1 = 𝟏𝟐𝒅𝑸/𝑻

For unit mass;

S = ms

And for any reversible process,

Q = 𝟏𝟐𝑻𝒅𝒔

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Entropy (cont’d)

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Fig 4: A series of constant entropy and constant temperature lines on a p-v diagram

The T-s diagram

A temperature entropy diagram, or T-s diagram, is used in thermodynamics to visualize changes to temperature and specific entropy during a thermodynamic process or cycle.

It helps to visualize the heat transfer during a process.For reversible (ideal) processes, the area under the T-s curve of a process is

the heat transferred to the system during that process.

By definition of entropy, the heat transferred to or from a system equals to the area under the T-s curve of the process.

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Its useful to plot lines of constant pressure and constant volume on a T-s diagram for a perfect gas.

Since changes of entropy are of more direct application than the absolute value, the zero of entropy can be chosen at any arbitrary reference temperature & pressure.

From Fig 6; let points A & B be at T2 and v1, and T2 & P1 respectively as shown.

sA – s1 = 𝟏𝑨𝒅𝑸/𝑻

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The T-s diagram for a perfect gas

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Fig 6: Entropy changes at constant Pressure & at constant volume for a

perfect gas on T-s diagram

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And at constant volume for 1kg of gas, from Equation; dQ = cv dT

Therefore

sA – s1 = 𝟏𝑨

cv𝒅𝑻/𝑻

= cv ln(TA /T1 )

= cv ln(T2 /T1 )

Similarly, at constant pressure for 1kg of gas, from Equation; dQ = cp dT

Hence

sB – s1 = 𝟏𝑩

cp𝒅𝑻/𝑻

= cp ln(TB /T1 )

= cp ln(T2 /T1 )

Example 4.3

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The T-s diagram for a perfect gas (cont’d)

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Fig 7: Constant Pressure & constant volume lines plotted on a T-s diagram for a

perfect gas

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Reversible isothermal Process

A reversible isothermal process will appear as a horizontal line on a T-s diagram, and the area under the line must represent the heat flow during the process.

Fig 7; shows a reversible isothermal expansion of wet steam into the superheat region.The shaded area represents the heat supplied during the process. i.e.

Heat supplied = T(s2 – s1 )

The absolute temp must be used.

Example 4.4

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Reversible Processes on T-s diagram

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Fig 8: Reversible isothermal process for steam on a T-s diagram

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• A reversible isothermal process for a perfect gas is shown on T-s diagram in Fig 9.• The shaded area represents the heat supplied during the process, i.e.

Q = T(s2 – s1 )

For a perfect gas undergoing isothermal process it is possible to remove

s2 – s1. AS from non flow equation, for a reversible process;

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Reversible Processes on T-s diagram (cont’d)

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Fig 9: Reversible isothermal process for a perfect gas

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Reversible Processes (isothermal process) on

T-s diagram (cont’d)

As

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Reversible Processes (isothermal process) on

T-s diagram (cont’d)

Example 4.5

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For a reversible adiabatic process the entropy remains constant, and hence the process is called an isentropic process.

For a process to be isentropic it need not to be either adiabatic or reversible, but the process will always appear as a vertical line on T-s diagram.

An isentropic process for superheated steam expanding into the wet region is shown in Fig. 10.

Example 4.6

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Reversible Processes (adiabatic process) on

T-s diagram (cont’d)

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Fig 10: Isentropic process for steam on a T-s diagram

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Fig 11: Isentropic process for a perfect gas on a T-s diagram

Read Polytropic process, & its T-s diagram

Example 4.7

Example 4.8

Example 4.9

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Reversible Processes on T-s diagram (cont’d)

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Entropy & irreversibility

Since entropy is a property, the change of entropy depends only on the end states and not on the process between the states.

Therefore,

Provided an irreversible process gives enough information to fix the end states then the change of entropy can be found.

Example 4.10

Example 4.11

Example 4.12

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Exergy

The theoretical maximum amount of work that can be obtained from a system at any state p1 & T1 when operating with a reservoir at the constant pressure and temperature p0 and T0 is called exergyor availability.

Reading assignment

Read for non-flow and steady-flow systems.

Effectiveness

Example 4.13

Example 4.14

Example 4.15

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Questions ?

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