First Law Thermo

8/14/2019 First Law Thermo

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Thermodynamics M. D. Eastin

First Law of Thermodynamics

ValveOpen

AirAir

What energy

transformations occur as

air parcels move around

within thunderstorms?


2/27


Outline:

Forms of Energy

Energy Conservation

Concept of Work

PV DiagramsConcept of Internal Energy

Joules Law

Thermal Capacities (Specific Heats)

Concept of Enthalpy

Various Forms of the First Law

Types of Processes



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Forms of Energy

Energy comes in a variety of forms

Potential

Mechanical Chemical Electrical

Internal Kinetic

Heat


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Energy Conservation

The First Law of Thermodynamicsstates that total energy is conserved for any

thermodynamic system energy can not be created nor destroyed energy can only change from one form to another

constant)( EEnergy

constantelectricalchemicalheat

mechanicalpotentialkineticinternal

EEE

EEEE

Our main concern in meteorology


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The Concept of Work

Workis a Mechanicalform of Energy:

DistanceForceWork

xFdW

Force

Distance

x


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The Concept of Work

Workis a Mechanicalform of Energy:

Recall the definition of pressure:

We can thus define work as:

DistanceForceWork

xFdW

2AreaForce

px

F

pdVdW


7/27Thermodynamics M. D. Eastin

The Concept of Work

Changes in Volume Cause Work:

Work is performed when air expands

Work of Expansion:

Occurs when a system performs work

(or exerts a force) on its environment

Is positive:

Rising air parcels (or balloons) undergo expansion work

Since the environmental pressure decreases with height,

with height a rising parcel must expand

to maintain an equivalent pressure

0dW

F



The Concept of Work


Similar to a piston in a car engine

FF



The Concept of Work


Work is performed when air contracts

Work of Contraction:

Occurs when an environment performs work

(or exerts a force) on a system

Is negative:

Sinking air parcels (or balloons) undergo contraction work

Since the environmental pressure decreases with height,

with height a sinking parcel must contract

to maintain an equivalent pressure

0dW

FF



Pressure-Volume (PV) Diagrams

Another Way of Depicting Thermodynamic Processes:

Consider the transformation: i f

p

VVfVi

pi

pf

i

f



Another Way of Depicting Work:

Consider the transformation: i f

p

V

pdVdW

f

ipdVW

VfVi

pi

pf

i

f The work done is the area

under the i f curve

(or gray area)

Pressure-Volume (PV) Diagrams



Internal Energy= Kinetic Energy +Potential Energy

(of the molecules in the system)Depends onlyon the current system state (p,V,T)Does notdepend on past statesDoes notdepend on how state changes occur

Changes are the result of external forcingon the system (in the form of workor heat)


tenvironmentenvironmeninternal HeatWorkE

dQdWdU

dQpdVdU



Joules Law

Valve

Closed

AirVacuum

Thermally Insulated System



Joules Law

Thermally Insulated System

Valve

Open

AirAir



Joules Law

dQpdVdU

Valve

Open

AirAir

Air expanded to fill the container

Change in volumeChange in pressure

No external work was done

Air expanded into a vacuum

within the system

No heat was added or subtract

Thermally insulated system

No change in internal energy

No change in temperature

What does this mean?

0dU



Joules Law

dQpdVdU

Valve

Open

AirAir

Air expanded to fill the container

Change in volumeChange in pressure

No external work was done

Air expanded into a vacuum

within the system

No heat was added or subtract

Thermally insulated system

No change in internal energy

No change in temperature

Internal Energy is only a function oftemperature

0dU U(T)U




Assume: A small quantity of heat (dQ) is given to a parcel

The parcel responds by experiencing a small temperature increase (dT)

Specific Heat (c):

Two Types of Specific Heats:

Depends on how the material changes as it receives the heat

Constant Volume:

Constant Pressure:

volumeconstant

vdT

dQc

Parcel experiences no

change in volume

Parcel experiences no

change in pressure

pressureconstant

pdT

dQc

dT

dQc




Specific Heat at Constant Volume:

Starting with:

If the volume is constant (dV = 0), we can re-write the first law as:

And substitute this into our specific heat equation as

volumeconstant

vdT

dQc

dQpdVdU dQdU

dT

dUcv or dTcdU v




Specific Heat at Constant Volume:

Since the internal energy is a state variable and does not depend on past statesor how state changes occur, we can define changes in internal energy as:

Also, if we substitute our specific heat equation into the first law:

We can obtain an alternative formof the First Law of Thermodynamics:

2

2

dTcU vT

T

pdVdTcdQ v

dQpdVdU dTcdU v




Specific Heat at Constant Pressure:

Starting with

and recognizing that,

we can obtain another alternative formof the First Law of Thermodynamics:

Also,

pressureconstant

pdT

dQc

pdVdTcdQ v

VdppdVd(pV)

VdpdTcdQ p

*

vp nRcc

TnRpV *



Concept of Enthalpy

Assume: Heat (dQ) is added to a system at constant pressure

Impact: 1) The systems volume increases (V1V2) and work is done

2) The systems internal energy increases (U1U2)

Using the First Law:

We can then define Enthalpy (H)as:

)V-p(VdW 12

12 U-UdU

1212

VVpUUdQ

pVUH


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Concept of Enthalpy

Enthalpy:

If we differentiate the definition of enthalpy and use prior relationships, we can

obtain the following relation:

We shall see that Enthalpywill be a useful concept since most sources and

sinks of heating in the atmosphere occur at roughly constant pressure

1212 VVpUUdQ

pVUH

dTcdHdQ p


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Forms of the First Law of Thermodynamics

For a gas of mass m For unit mass

dWdUdQ pdVdUdQ

pdVdTcdQ v

VdpdTcdQ p

dwdudq pddudq

pddTcdq v

dpdTcdq p

where: p = pressure U = internal energy

V = volume W = work

T = temperature Q = heat energy

= specific volume n = number of moles

cv= specific heat at constant volume (717 J kg-1K-1)

cp= specific heat at constant pressure (1004 J kg-1K-1)

Rd= gas constant for dry air (287 J kg-1K-1)

R* = universal gas constant (8.3143 J K-1mol-1)

nRcc *vp Rcc dvp


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Types of Processes

Isobaric Processes:

Transformations at constant pressuredp = 0

Isochoric Processes:

Transformations at constant volume

dV = 0d= 0

p

V

i f

p

V

i

f


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Types of Processes

Isothermal Processes:

Transformations at constant temperaturedT = 0

Adiabatic Processes:

Transformations without the exchange of heat

between the environment and the systemdQ = 0

More on this next lecture

p

V

i

f


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Summary:

Forms of Energy (know the seven types)Energy Conservation (know the basic concept)

Concept of Work (expansion and contraction in the atmosphere)

PV Diagrams (origins of an equation for Work)

Concept of Internal Energy (know the basic concept)

Joules Law (know what it implies to internal energy)


Concept of Enthalpy (know the basic concept)

Various Forms of the First Law

Types of Processes (isobaric, isothermal, isochoric, adiabatic)



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References

Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.

Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp.

Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.

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First Law Thermo