Lecture 3 – The First Law (Ch. 1)Lecture 3 – The First Law (Ch. 1)Friday January 11Friday January 11thth

•Test of the clickers (HiTT remotes)

•I will not review the previous class•Usually I will (certainly after Ch. 2)

•Internal energy

•The equivalence of work and heat

•The first law (conservation of energy)

•Functions of state

•Reversible workReading: Reading: All of chapter 1 (pages 1 - 23)All of chapter 1 (pages 1 - 23)

1st homework set due next Friday 1st homework set due next Friday (18th).(18th).

Homework assignment available on web Homework assignment available on web page.page.

Assigned problems: 2, 6, 8, 10, 12Assigned problems: 2, 6, 8, 10, 12

Functions of state: internal energy Functions of state: internal energy UU

Joule’s paddle wheelexperiment

Work = Ugrav

W = (mgh) = mgh

Gravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.

Adiabatic

Measured as a change Measured as a change in temperature, in temperature,

Functions of state: internal energy Functions of state: internal energy UU

Joule’s paddle wheelexperiment

Gravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.

Ufluid = W = mgh

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Adiabatic

Measured as a change Measured as a change in temperature, in temperature,

Functions of state: internal energy Functions of state: internal energy UU

Stirring

U = W = torque × angular displacement = d

Adiabatic

Rise in Rise in (temperature)(temperature)

Functions of state: internal energy Functions of state: internal energy UU

Electricalwork

U = W = i 2R

RRii

Adiabatic

Rise in Rise in (temperature)(temperature)

Functions of state: internal energy Functions of state: internal energy UU

Reversiblework

U = W = Force × distance = P V

Adiabatic

Rise in Rise in (temperature)(temperature)

Force, F

Equivalence of work and heatEquivalence of work and heat

Heat, Q

U = Q

Adiabatic

Same rise in Same rise in (temperature)(temperature)

The First Law of ThermodynamicsThe First Law of ThermodynamicsThese ideas lead to the first law of thermodynamics (a fundamental postulate):

“The change in internal energy of a system is equal to the heat supplied plus the work done on the system. Energy is conserved if the heat is taken into account.”

Note that đQ and đW are not functions of state. However, dU is, i.e. the correct combination of đQ and đW which, by themselves are not functions of state, lead to the differential internal energy, dU, which is a function of state.

U = Q U = Q ++ W W oror dUdU = = đđQQ đđW W

How to know if quantity is a function of How to know if quantity is a function of statestate

U1

U2

area under curveW PdV

U đQ + đWHow can U be state function, but not W?Heat is involved (not adiabatic).

Significantheat flows in

How to know if quantity is a function of How to know if quantity is a function of statestateThere is a mathematical basis.....There is a mathematical basis.....

Consider the function F = f(x,y):y x

f fdF dx dy

x y

z

y

x

dS

dr

dF

In general, F is a state function if the differential dF is ‘exact’. dF dF ((= Adx = Adx Bdy Bdy) is exact if:

1.

2. 0

3. is independent of pathb

a

A B

y x

dF

dF

See also: See also: •Appendix EAppendix E•PHY3513 notesPHY3513 notes•Appendix A in Carter bookAppendix A in Carter book

•In thermodynamics, all state variables are by definition exact. However, differential work and heat are not.

How to know if quantity is a function of How to know if quantity is a function of statestateThere is a mathematical basis.....There is a mathematical basis.....

Consider the function F = f(x,y):y x

f fdF dx dy

x y

Differentials satisfying the following condition are said to be ‘exact’:

0dF This condition also guarantees that any integration of dF will not depend on the path of integration, i.e. only the limits of integration matter.

This is by no means true for any function!

If integration does depend on path, then the differential is said to be ‘inexact’, i.e. it cannot be integrated unless a path is also specified. An example is the following:đF = ydx xdy.Note: is a differential đF is inexact, this implies that it cannot be integrated to yield a function F.

How to know if quantity is a function of How to know if quantity is a function of statestate