Thermodynamics

Thermodynamic Systems, States and Processes

Objectives are to:• define thermodynamics systems and states of systems• explain how processes affect such systems• apply the above thermodynamic terms and ideas to the laws of

thermodynamics

“Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium.

Internal Energy of a Classical ideal gas

At room temperature, for most gases:

monatomic gas (He, Ne, Ar, …) 3 translational modes (x, y, z)

kTEK2

3

diatomic molecules (N2, O2, CO, …) 3 translational modes (x, y, z) + 2 rotational modes (wx, wy)

kTEK2

5

pVkTNU2

3

2

3

Internal Energy of a Gas

pVkTNU2

3

2

3

A pressurized gas bottle (V = 0.05 m3), contains helium gas (an ideal monatomic gas) at a pressure p = 1×107 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?

J105.705.0105.1 537 mPa

Changing the Internal Energy

U is a “state” function --- depends uniquely on the state of the system in terms of p, V, T etc.

(e.g. For a classical ideal gas, U = NkT )

WORK done by the system on the environment

Thermal reservoir

HEAT is the transfer of thermal energy into the system from the surroundings

There are two ways to change the internal energy of a system:

Work and Heat are process energies, not state functions.

Wby = -Won

Q

Work Done by An Expanding Gas

The expands slowly enough tomaintain thermodynamic equilibrium.

PAdyFdydW

Increase in volume, dV

PdVdW +dV Positive Work (Work isdone by the gas)

-dV Negative Work (Work isdone on the gas)

A Historical Convention

Energy leaves the systemand goes to the environment.

Energy enters the systemfrom the environment.

+dV Positive Work (Work isdone by the gas)

-dV Negative Work (Work isdone on the gas)

Total Work Done

PdVdW

f

i

V

V

PdVW

To evaluate the integral, we must knowhow the pressure depends (functionally)on the volume.

Pressure as a Function of Volume

f

i

V

V

PdVW

Work is the area underthe curve of a PV-diagram.

Work depends on the pathtaken in “PV space.”

The precise path serves to describe the kind of process that took place.

Different Thermodynamic Paths

The work done depends on the initial and finalstates and the path taken between these states.

Work done by a Gas

Note that the amount of work needed to take the system from one state to another is not unique! It depends on the path taken.

We generally assume quasi-static processes (slow enough that p and T are well defined at all times):

This is just the area under the p-V curve

f

i

V

Vby dVpW

V

p p

V

p

V

dWby = F dx = pA dx = p (A dx)= p dV

Consider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is:

dx

When a gas expands, it does work on its environment

What is Heat?

Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system

Sign of Q : Q > 0 system gains thermal energyQ < 0 system loses thermal energy

Up to mid-1800’s heat was considered a substance -- a “caloric fluid” that could be stored in an object and transferred between objects. After 1850, kinetic theory.

A more recent and still common misconception is that heat is the quantity of thermal energy in an object.

The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir …

(like cash transfers into and out of your bank account)

Q U

An Extraordinary Fact

The work done depends on the initial and finalstates and the path taken between these states.

BUT, the quantity Q - W does not dependon the path taken; it depends only on the initial and final states.

Only Q - W has this property. Q, W, Q + W,Q - 2W, etc. do not.

So we give Q - W a name: the internal energy.

-- Heat and work are forms of energy transfer and energy is conserved.

The First Law of Thermodynamics

(FLT)

U = Q + Won

work doneon the system

change intotal internal energy

heat added

to system

or

U = Q - Wby

State Function Process Functions

1st Law of Thermodynamics

• statement of energy conservation for a thermodynamic system

• internal energy U is a state variable• W, Q process dependent

system done work : positive

system addedheat : positive

by

to

W

Q

WQU

The First Law of Thermodynamics

bydWdQdE int

What this means: The internal energy of a systemtends to increase if energy is added via heat (Q)and decrease via work (W) done by the system.

ondWdQdE int

. . . and increase via work (W) done on the system.

onby dWdW

Isoprocesses

• apply 1st law of thermodynamics to closed system of an ideal gas

• isoprocess is one in which one of the thermodynamic (state) variables are kept constant

• use pV diagram to visualise process

Isobaric Process• process in which pressure is kept

constant

Isochoric Process• process in which volume is kept

constant

Isothermal Process• process in which temperature is held

constant

Isochoric (constant volume)

Thermodynamic processes of an ideal gas( FLT: DU = Q - Wby )

V

p

1

2

pVTNkU

0pdVWby

FLT: UQ Q

Temperature changes

Isobaric (constant pressure)

V

p

1 2

VpTNkU FLT: VpWUQ by 1

VppdVWby

Q

p

Temperature and volume change

Isothermal (constant temperature)

2

1

V

V 1

2by V

VnNkTdVpW

0U

FLT: byWQ

p

V

1

2

( FLT: DU = Q - Wby )

V

1p

Q

Thermal Reservoir

T

Volume and pressure change