References: Tipler; wikipedia,…

Thermodynamics II

The First Law of Thermodynamics

• Heat and Work. First Law of Thermodynamics

• Heat and Work on Quasi-Static Processes for a Gas.

The Second Law of Thermodynamics

• Heat Engines and the Second Law of Thermodynamics

• Refrigerators and the Second Law of Thermodynamics

• The Carnot Engine

• Heat Pumps

• Irreversibility and disorder. Entropy

The First Law of Thermodynamics

System

Surroundings The system can exchange mass and energy through the boundary with the environment.

An example of “closed system” - no mass flow- is the gas confined in a cylinder. The boundary –in this case real wall- is made by the cylinder and the piston walls.

Energy exists in many forms, such as mechanical energy, heat, light, chemical energy, and electrical energy. Energy is the

ability to bring about change or to do work.

Thermodynamics is the study of energy.

The boundary of the system is arbitrarily chosen

The First Law of Thermodynamics

First Law of Thermodynamics → Conservation of Energy: Energy can be changed from one form to another, but it cannot be created or

destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another.

The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence,

energy can be converted from one form into another.

The energy balance of a system –as a consequence of FLT- is a powerful tool to analyze the exchanges of energy between the system

and its environment.

We need to define the concept of internal energy of the system, Eint as an energy stored in the system.

Warning: It is not correct to say that a system has a large amount of heat or a great amount of work

http://www.emc.maricopa.edu/faculty/farabee/BIOBK/BioBookEner1.html

The First Law of Thermodynamics. Heat, Work and Internal Energy

Joule’s Experiment and the First Law of Thermodynamics. Equivalence between work and heat

Schematic diagram for Joule´s experiment. Insulating walls are

necessary to prevent heat transfer from the enclosed water to the

surroundings.

As the weights fall at constant speed, they turn a paddle wheel, which does

work on water.

If friction in mechanism is negligible, the work done by the paddle wheel on

the water equals the change of potential energy of the weights.

1 calorie = 4.184 JoulesWork is done on water. The energy is transferred to the water – i. e. the system- . The energy transferred appears as an increase in temperature.

We can replace the insulating walls by conducting walls. We can transfer heat through the walls to the system to produce the same increase in temperature.

The increase in temperature of the system is a consequence of an increase in Internal Energy. Internal energy is a state function of the system

The sum of the heat transferred into the system and the work done on the

system equals the change in the internal energy of the system

onin WQE int

The First Law of Thermodynamics

Another method of doing work. Electrical work is done on the system by the generator, which is driven by the falling weight.

The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston

How does the confined gas exchange energy (heat and work) with the surroundings?.

How can we calculate the energy –heat and/or work- transferred, added or subtracted, to the system?

What is the value of the internal energy for the gas in the cylinder?

onin

onin

WQdEWQE

int

int

The state of the gas will be described by the Ideal Gas Law.

TRnPV

“Quasi static processes”: a type of process where the gas moves through a series of equilibrium states. Then, we can apply the Ideal Gas Law. In practice, if we move the piston slowly, it will be possible to approximate quasi-static processes fairly well.

First Law

HλET

CO2

Rn = Rns + Rnl

D

G

ΔE Ph

Ph

Net fluxes of mass Water vapor Carbon –CO2

Energy fluxes: Rn : Net gain of heat energy from radiation λET Latent heat, Energy associated to the flux of water vapor leaving from the system H Sensible Heat. G Heat energy by conduction to the soil

Ph: Net photosynthesis ΔEint: Change of the internal energy of the system D: Advection

First Law of Thermodynamics. Fluxes of energy and mass on the earth surface. Energy balance.

Energy balance (applying First Law):

Rn – H – λET – G – D - Ph = ΔEint

The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston

Internal Energy for an Ideal Gas. It only depends on the temperature of the gas, and not on its volume nor its pressure Experiment: Free expansion.

For a gas at low density – an ideal gas-, a free expansion does not change the temperature of the gas.

What is the value of the internal energy for the gas in the cylinder?

If heat is added at constant volume, no work is done, so the heat added equals to the increase in thermal energy

dTcndTCdE

TCQQE

VV

and

Vin

in

int

int

Internal Energy is a state function, i.e. it is not dependent on the process, it only depends of the initial and final temperature

Heat transferred to a system

The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston

If heat is added at constant volume, no work is done, so the heat added equals the increase in thermal energy

TcnTCQ

dTcndTCQ

VVVin

VVVin

,

,

If heat is added at constant pressure the heat energy transferred will be used to expand the substance and to increase the internal energy.

If the substance expands, it does work on its surroundings.

The expansion is usually negligible for solids and liquids, so for them CP ~ CV.

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PP

PP

RnCC

dTCCPdVPdVdTCWQdE

VP

dPconstPandVdPPdVPVdas

VP

PonP

0)(

int

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Applying the First Law of Thermodynamics

Heat transferred to a system. A summary

The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston

Heat energy can be added to (or lost from) the system. The value of the heat energy transferred depends on the process.

Typical processes are

- At constant volume

- At constant pressure

For the case of ideal gas

dTCQTCQ VVVV ;

For solids and liquids, as the expansion at constant pressure is usually negligible CP ~ CV.

dTCQTCQ PPPP ;

RnCC VP Relationship of Mayer

From the Kinetic theory, for monoatomic gases

for biatomic gases

Adiabatic: A process in which no heat flows into or out of a system is called an adiabatic process. Such a process can occur when the system is extremely well insulated or when the process happens very quickly.

Ide

al G

as

RnCV 2

3

RnCV 2

5

Work done on the system, Won , is the energy transferred as work to the system.

When this energy is added to the system its value will be positive.

The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston

The work done on the gas in an expansion is

)( 21

2

1

VVPdVPWV

Vgason

P- V diagramsConstant pressure

gasbygason

V

Vgason

WW

dVPW

2

1

If 5 L of an ideal gas at a pressure of 2 atm is cooled so that it contracts at constant pressure until its volume is 3 L what is the work done on the gas? [405.2 J]

The First Law of Thermodynamics. P-V diagrams

)( 21

2

1

VVPdVPWV

Vgason

P- V diagrams

Conecting an initial state and a final state by three paths

Isothermal

Constant pressure

Constant Volume

Constant Temperature

02

1

V

Vgason dVPW

1

2ln2

1 V

VTRndV

V

TRnW

V

Vgason

The First Law of ThermodynamicsA biatomic ideal gas undergoes a cycle starting at point A (2 atm, 1L). Process from A to B is an expansion at constant pressure until the volume is 2.5 L, after which, it is cooled at constant volume until its pressure is 1 atm. It is then compressed at constant pressure until the volume is again 1L, after which it is heated at constant volume until it is back to its original state. Find (a) the work, heat and change of internal energy in each process (b) the total work done on the gas and the total heat added to it during the cycle.

A system consisting of 0.32 mol of a monoatomic ideal gas occupies a volume of 2.2 L, at a pressure of 2.4 atm. The system is carried through a cycle consisting:

1. The gas is heated at constant pressure until its volume is 4.4L.

2. The gas is cooled at constant volume until the pressure decreases to 1.2 atm

3. The gas undergoes an isothermal compression back to its initial point.

(a) What is the temperature at points A, B and C

(b) Find W, Q and ΔEint for each process and for the entire cycle

The First Law of Thermodynamics. Processes. P-V Diagrams

Adiabatic Processes. No heat flows into or out of the system

The First Law of Thermodynamics. Processes. P-V Diagrams

Adiabatic Processes. No heat flows into or out of the system

1,

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VPVPW

TcnWEthenprocessAdiabaticQ

Vadiabaticon

in

,int

0

constPTconstVT

tcoefficienadiabaticC

CconstVP

V

P

1

1

;

The equation of curve describing the adiabatic process is

We can use the ideal gas to rewrite the work done on the gas in an adiabatic process in the form

A quantity of air is compressed adiabatically and quasi-statically from an initial pressure of 1 atm and a volume of 4 L at temperature of 20ºC to half its original volume. Find (a) the final pressure, (b) the final temperature and (c) the work done on the gas. cP = 29.19 J/(mol•K); cV = 20.85 J/(mol•K). M=28.84 g

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

Two moles of an ideal monoatomic gas have an initial pressure P1 = 2 atm and an initial volume V1 = 2 L. The gas is taken through the following quasi-static cycle:

A.- It is expanded isothermally until it has a volume V2 = 4 L.

B.- It is then heated at constant volume until it has a pressure P3= 2 atm

C.- It is then cooled at constant pressure until it is back to its initial state.

(a) Show this cycle on a PV diagram. (b) Calculate the heat added and the work done by the gas during each part of the cycle. (c) Find the temperatures T1, T2, T3

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

At point D in the figure the pressure and temperature of 2 mol of an ideal monoatomic gas are 2 atm and 360 K. The volume of the gas at point B on the PV diagram is three times that at point D and its pressure is twice that at point C. Paths AB and DC represent isothermal processes. The gas is carried through a complete cycle along the path DABCD. Determine the total work done by the gas and the heat supplied to the gas along each portion of the cycle

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams