Lecture 25

Thermodynamics

Today’s Topics:

• 0th and 1st and Laws of Thermodynamics• Thermal Processes and Ideal Gases• Heat Capacities

Thermodynamic Systems

Thermodynamics is the branch of physics that is built upon the fundamental laws that heat and work obey.

The collection of objects on which attention is being focused is called the system, while everything elsein the environment is called the surroundings.

Walls that permit heat flow are called diathermal walls,while walls that do not permit heat flow are calledadiabatic walls.

To understand thermodynamics, it is necessary to describe the state of a system.

The 0th LawTwo systems are said to be in thermal equilibrium if there is no heat flowbetween them when they are brought into contact.

Temperature is the indicator of thermal equilibrium in the sense that there is nonet flow of heat between two systems in thermal contact that have the sametemperature.

THE ZEROTH LAW OF THERMODYNAMICS

Two systems individually in thermal equilibriumwith a third system are in thermal equilibriumwith each other.

The 1st Law – Energy Conservation

Suppose that a system gains heat Q and that is the only effect occurring.

Consistent with the law of conservation of energy, the internal energy of the system changes:

QUUU if =-=D

Q > 0,when the system gains heat and Q < 0,when the system loses heat.

If a system does work Won its surroundings and there is no heat flow, conservation of energy indicates that the internal energy of the system will decrease:

WUUU if -=-=D

W > 0, when done by the systemand W < 0, when done on the system.

THE FIRST LAW OF THERMODYNAMICS

The internal energy of a system changes due to heat and work:

WQUUU if -=-=D

Work is positive when it is done by the system and negative when it is doneon the system.

Heat is positive when the system gains heat and negative when the systemloses heat.

Positive and Negative Work

In part a of the figure, the system gains 1500J of heatand 2200J of work is done by the system on its surroundings.

In part b, the system also gains 1500J of heat, but2200J of work is done on the system.

In each case, determine the change in internal energyof the system.

(a)

( ) ( ) J J J 70022001500 -=+-+=-=D WQU

(b)

( ) ( ) J J J 370022001500 +=--+=-=D WQU

ExampleAn ideal gas absorbs 750 J of heat as it performs 625 J of work. What is the resulting change in temperature if there are 1.3 moles of an ideal gas in the system?

J 750+=Q

J 625+=W

Thermal Processes

A quasi-static process is one that occurs slowly enough that a uniformtemperature and pressure exist throughout all regions of the system at alltimes.

isobaric: constant pressure

isochoric: constant volume

isothermal: constant temperature

adiabatic: no transfer of heat

An isobaric process is one that occurs at constant pressure.

VPPAsFsW D===

W

An isochoric process is one that occurs at constant volume.

QWQU =-=D

0=W

Thermal processes using an ideal gasISOTHERMAL EXPANSION OR COMPRESSION

The hot water provides a reservoir of heat that maintains the cylinder at a constant temperature

As the force holding the piston is reduced, the gas expands from an initial volume Vi to a final volume Vf

ExampleA system containing an ideal gas at a constant pressure of 1.22 × 105 Pa gains 2140 J of heat. During the process, the internal energy of the system increases by 2320 J. What is the change in volume of the gas?

Pa 51022.1 ´=PJ 2140+=Q

J 2320+=DU

ExampleA fixed amount of ideal gas is compressed isothermally. Which entry in the table below correctly depicts the signs of the work done, the change in the internal energy, and the heat exchanged with the environment?

work done change in internal energy heat exchanged(a) negative zero negative(b) positive negative zero(c) negative zero positive(d) negative negative zero(e) positive zero positive

For an isothermal process:

Compression means work is done on gas:

Using the 1st Law:

Specific Heat CapacitiesTo relate heat and temperature change in solids and liquids, we used:

TmcQ D=

specific heatcapacity

The amount of a gas is conveniently expressed in moles, so we write thefollowing analogous expression:

TnCQ D=

molar specificheat capacity

For gases we distinguish between the molar specific heat capacities which apply to the conditions of constant pressure and constant volume:

PV CC ,

Why?

In a constant volume process, all of the heat added goes towards changing the temperature of the system.

In a constant pressure process, the heat added to the system increases the temperature and doing mechanical work.

( ) TnRTTnRWUQ if D=+-=+D= 23

23

olumeconstant v 0!"!#$

!!!! %!!!! &'First law ofthermodynamics

constant volumefor a monatomicideal gas

CV

CP

( ) ( ) TnRTTnRTTnRWUQ ifif D=-+-=+D= 25

23

pressureconstant !"!#$

!%!&'

!!!! "!!!! #$

First law ofthermodynamics

constant pressurefor a monatomicideal gas

For an Ideal Gas

Adiabaticexpansion orcompression ofa monatomicideal gas ( )fi TTnRW

WΔUQSince

-=-==

23

,0

Adiabaticexpansion orcompression ofa monatomicideal gas

ggffii VPVP =

VP cc=g

ADIABATIC EXPANSION OR COMPRESSION

DEMO: Adiabatic compression