Thermodynamics

Definitions• Thermodynamics is the study of processes in

which energy is transferred as work and heat• The system is a set of particles we wish to study• The environment is everything else• Heat (Q) is the transfer of energy into or out of

the system by a temperature difference• Work (W) is the transfer of energy into or out of

the system by a force• Internal energy (U) is the sum of the kinetic and

potential energies of all the particles in the system

Diagram

• This diagram summarizes these concepts:

SystemHeat, Q Work, W

U

Environment

SystemBoundary

Types of Systems

• An open system allows mass and energy to enter or leave

• A closed system does not allow mass to enter or leave (but energy can)

• An isolated system does not allow energy (in any form) to enter or leave

First Law of Thermodynamics• Let Q be positive when heat is absorbed by the

system• Let W be positive when the system does work on

the environment• The first law of thermodynamics says that for a

closed system:U = Q W

SystemW

UQ

Understanding the First Law• There are only two ways for energy to transfer

into or out of a closed system: heat and work• The first law is a statement of conservation of

energy• Note that the sign of Q and W depend on the

direction of energy transfer:Signs of Q and W for a System

Q > 0 Energy added to system as heat

Q < 0 Energy removed from system as heat

Q = 0 No transfer of energy as heat

W > 0 Work done by system (expansion of gas)

W < 0 Work done on system (compression of gas)

W = 0 No work done

Example

Q: What is the change in the internal energy of a gas that releases 489 J of heat while simul-taneously being compressed by 731 J of work?

A: U = ? Q = -489 J, W = -731 JU = Q W = (-489 J) (-731 J)

= 242 J

GasU = 242 J

W = -731 J

Q = -489 J

Gases and the First Law• The first law allows us to study processes

involving gases• An ideal gas has the following state variables:

• Pressure is defined as force per area:P = F/A (SI unit: 1 Pa = 1 N/m2)

variable name units

P pressure Pa (= N/m2)V volume m3 T temperature K

n # of moles molU internal energy J

P-V Diagrams• A pressure-volume diagram lets us track the

state of a gas as it goes through a processpr

essu

re (P

a)

volume (m3)

Initial state

final state

(Pi, Vi)

(Pf, Vf)

• Pressure and volume specify the entire state of a gas under the following conditions:– gas is ideal and has the following state equation:

PV = nRT [R = 8.314 J/(molK)]– gas does not change phase nor undergo reaction

U = (constant) T– system is closed so that

n = constant• A P-V diagram lets us track the state of a gas as

energy is transferred as heat and work

Types of Thermodynamic Processes• A gas undergoing an isobaric process is at

constant pressure

The work done by the gas is W = PVU = Q PV

pres

sure

(Pa)

volume (m3)

(P,Vi) (P,Vf)

T1

T2

T3

• A gas undergoing an isovolumetric process is at constant volume

W = 0U = Q

pres

sure

(Pa)

volume (m3)

(Pf, V)

T1

T2

T3

(Pi, V)

• A gas undergoing an isothermal process is at constant temperature

U = 0 Q = W

pres

sure

(Pa)

volume (m3)T1

T2

T3

isotherms

• A gas undergoing an adiabatic process does not absorb or release any heat (Q = 0)

Q = 0U = -W

pres

sure

(Pa)

volume (m3)T1

T2

T3

Cyclic Processes• A cyclic process is one where the system

returns to its initial state after going through a series of changes in P, V, T, etc.– In the process of going through this cycle, the

system may transfer energy as heat and work– The change in internal energy for one cycle is zero

(Unet = 0)

• There are two classes of cyclic processes:– heat engines (use heat to produce work)– Refrigerators (use work to move heat from a cold

reservoir to a hotter one)

Heat Engines• The P-V diagram for a heat engine looks like this

• The process is clockwise• The work done by the system is proportional to the

area of the “eye”

pres

sure

(Pa)

volume (m3)T1

T2

T3H

eat i

n

Hea

t out

Heat from a high-temperature source (QH)

Waste heat transferred to a low-temperature reservoir (QL)

• Since Unet = 0 and Qnet = QH QL we have

Unet = Qnet Wnet

0 = Qnet Wnet

0 = QH QL Wnet

Wnet = QH QL • This diagram shows the energy flow for a heat engine:

Hot Source (TH)

Cold Sink (TL)

QL

QH

WnetHeat Engine

Efficiency of a Heat Engine• The efficiency of a heat engine is a measure of

how well the engine operates• The efficiency of a heat engine is defined as

eff = Wnet/QH

• This can be written as

eff = = 1 QH QL

QH

QL

QH

• Example:A steam engine takes in 2.25 × 104 kJ from the

boiler and gives up 1.92 × 104 kJ in exhaust every cycle.

a)How much work does the engine do every cycle?

Wnet = QH QL = 2.25 × 104 kJ 1.92 × 104 kJ

= 3.3 × 103 kJ b)What is the efficiency of the engine?eff = 1 QL /QH = 1 1.92 × 104 kJ / 2.25 × 104 kJ

= 0.15 or 15%

Second Law of ThermodynamicsAll the king’s horses and all the king’s men

Couldn’t put Humpty together again

• Many processes go only in one direction and cannot be reversed. Why?

• Even if the first law of thermodynamics is obeyed, certain things are never seen to happen:

ONE WAY

Shake-shake

– Heat is never observed to flow spontaneously from cold things to hot ones

– Broken coffee cups are never seen to spontaneously re-assemble and fly back up on the table

– Salt and pepper, once mixed, will never separate back into two layers of salt and pepper by shaking

HEAT

cold hot

Statements of the Second Law • There are many ways to state the second law of

thermodynamics, but the general idea is this:In all processes, a system tends to move from order to disorder and, in fact, the total disorder of the universe is always increasing

• What is the state of maximum disorder for an isolated system?– thermal equilibrium!

Isolated gas

T1 T2

More Order

T

Less Order (Thermal Equilibrium)

• A thermodynamic quantity called entropy is a measure of the disorder of a system

• A more scientific way of stating the second law is:In all processes, the entropy of a system tends to increase with time and, in fact the entropy of the universe is constantly increasing

• The second law can be understood in terms of probability: disordered states are far more numerous than ordered ones, and thus are far more likely to exist

The Second Law for Heat Engines

• The second law, when applied to heat engines, puts limits on their efficiency

• In fact the second law can be stated in terms of heat engines:No heat engine can be 100% efficient. In other words, the efficiency is always less than one, and the “waste heat”, QL , is never zero

• In equations:eff < 1 (never equal)QL > 0 (never equal)