work and heat

Work and Heat Dr. Rohit Singh Lather

Forms of Energy

Energy

Macroscopic Microscopic Kinetic Potential

Sensible(translational + rotational + vibrational)

Latent(inter molecular phase change)

Chemical(Atomic Bonds)

Atomic(bonds within nucleolus of atoms)

SummationofallthemicroscopicenergiesiscalledInternalEnergy

E=U+KE+PE(kJ)

LowGrade HighGradeHeat Work

24/08/16 Dr.RohitSinghLather- EngineeringThermodynamics 2

Introduction • Temperature determines the direction of flow of thermal energy between two

bodies in thermal equilibrium• Temperature is also a measure of the average kinetic energy of particles in a

substance• Changes in the state of a system are produced by interactions with the

environment through heat and work• Heat and work are two different modes of energy transfer• During these interactions, equilibrium (a static or quasi-static process) is

necessary for the equations that relate system properties to one-another to bevalid

Heat is the random motion of the particles in the gas, i.e. a

“degraded” from of kinetic energy

• Bodies don't “contain” heat• Heat is identified as it comes across

system boundaries• The amount of heat needed to go from

one state to another is path dependent


System

Surroundings

System System

Surroundings Surroundings

System at higher temperature looses energy as heat

System and surrounding at same temperature, no energy

is transferred as heat

System at lower temperature gains energy as heat

0,0,

=Δ=Δ

↑Δ↑Δ

ΔΔ

UTifUTif

TU α

All of the energy inside a system is called INTERNAL ENERGY

When you add HEAT (Q), you are adding energy and the internal energy INCREASES

QReleased = Negative (-) QAbsorbed = Positive (+)


Specific Heat• Note: It is easy to change the temperature of some things (e.g. air) and hard to change the

temperature of others (e.g. water, block of steel)• The amount of heat (Q) added into a body of mass m to change its temperature an amount is given

byQ= m.C.∆T = m.C.(Tf – Ti)

C is called the specific heat and depends on the material Note: Temperature in either Kelvin or Celsius

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟⎠

⎞⎜⎜⎝

⎛=

Δ=

CkgJ

Cgcal

TmQC oo

The heat capacity C of an object is the proportionality constant between the heat Qthat the object absorbs or loses and the resulting temperature change ΔT of the object

# It is important to distinguish the heat transfer is done with constant volume or constant pressure The specific heat is different for different processes, particular for gases


Heat of Transformation

When the phase change is between liquid to gas, the heat of transformation is called the heat of vaporization LV

(# sublimation: transition from solid directly to gas phases)

The amount of energy per unit mass that must be transferred as heat when a sample completelyundergoes a phase change is called the heat of transformation L (or latent heat)

When a sample of mass m completely undergoes a phase change, the total energy transferred is:

When the phase change is between solid to liquid, the heat of transformation is called the heat of fusion LF

24/08/16 Dr.RohitSinghLather- EngineeringThermodynamics 6Source: Yunus A. Cengel and Michael A. Boles Thermodynamics: An Engineering Approach, McGraw Hill, 8th Edition

• The amount of energy needed to raise the temperature of a unit of mass of a substance by onedegree is called the specific heat at constant volume Cv for a constant-volume process:

• The amount of energy needed to raise the temperature of a unit of mass of a substance by onedegree is called the specific heat at constant pressure Cp for a constant pressure process:

3-31Heat Capacities at Constant Volume and Constant Pressure

• For ideal gases u, h, Cv, and Cp are functions of temperature alone

Source: Yunus A. Cengel and Michael A. Boles Thermodynamics: An Engineering Approach, McGraw Hill, 8th Edition24/08/16 Dr.RohitSinghLather- EngineeringThermodynamics 7

Experimental apparatus used by Joule

It has been demonstrated mathematically and experimentally (Joule, 1843) that for an ideal gas the internal energy is a function of the temperature only. That is, u = u(T)

Water

EvacuatedAir (high pressure)

Thermometer

• Joule’s reasoned, the internal energy is a function of temperature only and not a function ofpressure or specific volume

• Later Joule’s showed that for gases that deviate significantly from ideal- gas behavior, theinternal energy is not a function of temperature alone

• Using the definition of enthalpy and the equation of state of an ideal gas, we have is also afunction of temperature only h = h(T)

Since u and h depend only on temperature for an ideal gas, the specific heats cv and cp also depend, at most, on temperature only. Therefore, at a given temperature, u, h, cv, and cp of an ideal gas have fixed values regard- less of the specific volume or pressure Thus, for ideal gases, the partial derivatives in Eqs. 4–19 and 4–20 can be replaced by ordinary derivatives. Then, the differential changes in the internal energy and enthalpy of an ideal gas can be expressed as u = u(T) For ideal gases, u, h, cv, and cp vary with temperature only

du = cv(T) dT

• For ideal gases Cv, and Cp are related by: Cp = Cv + R [kJ / (kg.K)]

• The specific heat ratio 𝛾 is defined as: 𝛾 = 𝑪𝒑𝑪𝒗

• For incompressible substances (liquids and solids), both the constant-pressure and constant-volume specific heats are identical and denoted by C:

Cp = Cv = C [kJ / (kg.K)]

Source: Yunus A. Cengel and Michael A. Boles Thermodynamics: An Engineering Approach, McGraw Hill, 8th Edition

Cp > Cv In an isobaric process system is heated and work is performed

CV CP

Monoatomic Gases %& R %

& R

Diatomic Gases %& R %

& R

Triatomic Gases %& R %

& R


Heat Transfer MechanismsConduction: (solids--mostly)

Heat transfer without mass transfer

Radiation Heat transfer through electromagnetic waves

Convection: (liquids/gas) Heat transfer with mass transfer due to motion


Conduction

If Q be the energy that is transferred as heat through theslab, from its hot face to its cold face, in time t, then theconduction rate Pcond (the amount of energy transferred perunit time) isTH

Hot Reservoir

TCCold

ReservoirQ

Slab of face area A &Thermal conductivity k

Thickness L

We assume steady state of heat transfer

Here k, called the thermal conductivity, is a constant that depends on the material of which the slab is made


Convection• In convection, thermal energy is transferred by bulk motion of materials from regions of high to

low temperatures• This occurs when in a fluid a large temperature difference is formed within a short vertical

distance (the temperature gradient is large)• Typically very complicated• Very efficient way to transfer energy


Radiation• Everything that has a temperature radiates energy• Method that energy from sun reaches the earth• In radiation, an object and its environment can exchange energy as heat via electromagnetic waves• Energy transferred in this way is called thermal radiation• The rate Prad at which an object emits energy via electromagnetic radiation depends on the

object’s surface area A and the temperature T of that area in K, and is given by

• Note: if we double the temperature, the power radiated goes up by 24 =16• If we triple the temperature, the radiated power goes up by 34=81

Stefan–Boltzmann constant5.6704 x10-8 W/m2 K4

Emissivity

If the rate at which an object absorbs energy via thermal radiation from its environment is Pabs, then the object’s net rate Pnet of energy exchange due to thermal radiation is


Quasi-Static Process • Arbitrarily slow process such that system always stays stays arbitrarily close to thermodynamic

equilibrium• Infinite slowness is the characteristics of a quasi-static process• It is a succession of equilibrium states• A quasi-static process is also reversible process

Dots indicate equilibrium states

Pres

sure

1

2

VolumeEvery state passed through by the system will be an equilibrium state

Such a process is locus of all the equilibrium points passed through by

the system

SystemBoundary

PistonWeight

FinalState

InitialState

MultipleWeights

FinalState

InitialState

Piston

dv

dp


Work • Heat is a way of changing the energy of a system by virtue of a temperaturedifference only• Other means for changing the energy of a system is called work• We can have push-pull work

- (e.g. in a piston-cylinder, lifting a weight)- electric and magnetic work (e.g. an electric motor)- chemical work, surface tension work, elastic work, etc.

• In defining work, we focus on the effects that the system (e.g. an engine) has onits surroundings

If work is done on the system the work is negative

(energy added to the system)

Work as being positive when the system does work on the surroundings

(energy leaves the system)


Pressure Volume Diagrams and Work Done

This area represents the work done by the gas

(on the surroundings) when it expands

from state A to state B

Pres

sure

Volume

Changes that happen during a thermodynamic process can usefully be

shown on a pV diagram


Work Done by a Gas (Constant Pressure)

Work = force x distance= force x Δx= PAΔx (Pressure = F/A so F = PA)= pΔV (AΔx = ΔV)

Q P

Δx

A

The

rmal R

eser

voir

ΔV

Pres

sure

VolumeV1 V2

PI = PF = P

24/08/16 Dr.RohitSinghLather- EngineeringThermodynamics 18Source: Yunus A. Cengel and Michael A. Boles Thermodynamics: An Engineering Approach, McGraw Hill, 8th Edition

• The “negative” sign in the equation for WORK is often misunderstood

• Since work done by a gas has a positive volume change we must understand that the gas itself is

USING UP ENERGY or in other words, it is losing energy, thus the negative sign

• When work is done ON a gas the change in volume is negative, this cancels out the negative sign in

the equation, this makes sense as some EXTERNAL agent is ADDING energy to the gas

W = - P ΔV

ΔV = Positive + Work done by System

ΔV = Negative (-) done on system

Work done by System is Negative (-)

Work done on system is Positive (+)


Expansion and Non-Expansion Work• Electrical work (kJ):• Boundary work (kJ):• Gravitational work (kJ):• Acceleration work (kJ) :• Shaft work (kJ):• Spring work (kJ):


POSITIVE WORK

LESS WORK

NEGATIVE WORK

MORE WORK

VolumePr

essu

reVolume

Pres

sure

W > 0

W > 0

Volume

Pres

sure

1

2

W > 0

Volume

1

2

W < 0

Pres

sure


Volume

Pres

sure

1

2

CYCLIC POSITIVE NET WORK

The work done on a system during a closed cycle can be non-zero

• To go from the state (Vi, Pi) by the path (a) to the state (Vf, Pf) requires a different amount of

work then by path (b).

• To return to the initial point (1) requires the work to be nonzero

Wnet > 0

Volume

Pres

sure

CONTROL WORK

The work done on a system depends on the path taken in the PV diagram


How do you change Internal Energy (∆U)

Q

Thermal Reservoir

Change in Volume

∆U = Q + W ∆U = Q - W Won the gas = – Wby the gas

Supplying Heat

Work

OR AS

The first law of thermodynamics (closed system) states that the change in internal energy (DU) is the sum of the work and heat changes: it is applicable to any process that begins and ends

in equilibrium states

All the energies received are turned into the energy of the system: this is a form of the energy conservation law


• Internal Energy (U) is a state function: a property that depends only on the current state of the system and is independent of how that state was prepared

• Energy can cross the boundaries of a closed system in the form of heat or work

• If the energy transfer across the boundaries of a closed system is dueto a temperature difference, it is heat; otherwise, it is work


Thermodynamic Processes - Ideal Gas Processes

• States of a thermodynamic system can be changed by interacting with its surrounding through work and heat. When this change occurs in a system, it is said that the system is undergoing a process.• A thermodynamic cycle is a sequence of different processes that begins and ends

at the same thermodynamic state.

• Some sample processes:− Isothermal Process: Temperature is constant T=C− Isobaric Process: Pressure is constant, P=C− Constant Volume Process: Volume is V=C− Adiabatic Process: No heat transfer, Q=0− Isentropic Process: entropy is constant, (n = 𝛾), s=C


Isothermal Process

Q = W

W = ∫ 𝑷𝒅𝑽𝟐𝟏

W = ∫ 𝒎𝑹𝑻𝑽 𝒅𝑽𝟐

𝟏

W = mRT∫ 𝒅𝑽𝑽

𝟐𝟏

Assumptions: Ideal gas(closed system)

W = mRT In 𝑽𝟐𝑽𝟏

W = mRT In 𝑷𝟏𝑷𝟐

ΔT = 0, then ΔU = 0

ΔU = Q - WWork done by System

ΔU = Q - WWork done by System

Q = WWork done by System

Isotherm

Pres

sure

1

2

VolumeV1 V2

To keep the temperature constant both the pressure and volume change to compensate (Volume

goes up, pressure goes down) “BOYLES’ LAW”

T2 = T1

Q

W

V1

V2

Internal Energy Does not Change


Reversible process can be reversed by an infinitesimal change in a variable

E.g. reversible, isothermal expansion of an ideal gas

Work done is the area beneath the ideal gas isotherm lying between the initial and

the final volumesPi

Pf

P=nRT/V

Vi Vf

Pres

sure

Volume

w


Isobaric Process

• In isobaric process P = C , then ∆U = Q – W

W = ∫ 𝑷𝒅𝑽𝟐𝟏

W = P∫ 𝒅𝑽𝟐𝟏

W = P (V2 – V1)

Heat is added to the gas which increases the Internal Energy (U)

∆U = Q - W can be used since the in this case Pr

essu

re

1 2

VolumeV1 V2

P2 = P1

Q

W = p (V2 – V1)

V1

V2

The path of an isobaric process is a horizontal line called an isobar

V2 – V1

p

Work is done by the gas as it changes in volume

T2 = T1


Isochoric / Isometric Process

• In isobaric process V = C ∆U = Q – W

W = ∫ 𝑷𝒅𝑽 = 𝟎𝟐𝟏

Ideal gas assumption (closed system)

Q = m.∆U = m∫ 𝑪𝑽𝒅𝑻𝟐𝟏

No work done

Since, ∆V = 0

∆U = Q – Wby

∆U = Q – 0

∆U = Q

Pres

sure

1

2

Volume

V1

V2 V2 = V1

QV2 = V1 W = 0

T2 > T1


Adiabatic Process

• Adiabatic process Q = 0 ∆U = Q – W

∆U = - W

dW = dU

Ideal gas assumption (closed system)

dU + PdV = 0 m.CV.dT + (3456 ) dV = 0

CV.dT + (456 ) dV = 0

5&57

= (𝑉1𝑉2

)(𝛾− 1)

Integrate and R = Cp - CvCv lnT + R lnV = C

(;<;= - 1)InV + In T = C

(𝛾 - 1)In V + In T = CInV (𝛾- 1)+ In T = C

In (T V (𝛾- 1)) = CT V (𝛾- 1)= C

T1 V1(𝛾- 1) = T2 V2

(𝛾- 1)

(infinitesimal increment of work and energy)

Pres

sure

1

2

VolumeV1 V2

Q = 0 V1

V2

T1 > T2

P,V, T Change

Adiabat

T1

T2

Wby = - ∆U

Loosing internal energy


5&57

= (𝑉1𝑉2

)(𝛾− 1)

PV= nRT T = PV/nRT1 V1(𝛾- 1)= T2 V2

(𝛾- 1)

>767?4 V1

(𝛾- 1)= >&6&?4 V2(𝛾- 1)

P1V1𝛾 = P2V2

𝛾

Relation of Temperature with Volume

Relation of Pressure with Volume


Polytropic Process • ”Polytropic" describes any reversible process on any open or closed system of gas or vapor which

involves both heat and work transfer, such that a specified combination of properties weremaintained constant throughout the process

• The expression relating the properties of the system throughout the process is calledthe Polytropic path

• Polytropic Process: its P-V relation can be expressed as

PVn = Constant (c)

Where, n is a constant for a specific process

- Isothermal, T = constant, if the gas is an ideal gas then P.V = R.T = constant, n = 1

- Isobaric, P = constant, n = 0 (for all substances)

- Constant-volume, V = constant, V = constant(P)(1/n), n =∞, (for all substances)

- Adiabatic Process, n = k for an ideal gas


PV Diagram for various Polytropic Processes

P1 V1𝛾 = P2 V2

𝛾 = PVn

W = ∫ 𝑷𝒅𝑽𝟐𝟏

W = ∫ 𝑷𝑽𝒏 𝑽⁻𝒏𝒅𝑽𝟐𝟏

W = 𝑷𝑽𝒏 ∫ 𝑽⁻𝒏𝒅𝑽𝟐𝟏

W = 𝑷𝑽𝒏

𝟏B𝒏 (𝑽𝟐𝟏B𝒏 −𝑽𝟏𝟏B𝒏)

W = 𝑷𝟐𝑽𝟐−𝑷𝟏𝑽𝟏

𝟏B𝒏

Pres

sure

Volume

n = 0

n = infinityn > 1

n = 1

n < 1

E𝑪𝑽𝒏

𝟐

𝟏𝐝𝐕


Polytropic

Adiabatic

Isothermal

Isobaric

Isochoric

In Summary

Process Important Point to Remember Gas Law that identifies itIsothermal Constant T, dU = 0, Q = W Boyles Law Isochoric Constant V, W = 0, dU = Q Charles LawIsobaric Constant P, dU = Q – ( - PdV) Gay – Lussac’s LawAdiabatic Nothing is Constant , Q = 0, dU = - W Combined Gas Law


Source: http://www.learneasy.info/MDME/MEMmods/MEM23006A/thermo/gases_files/gas_equations.png24/08/16 Dr.RohitSinghLather- EngineeringThermodynamics 35