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Thermodynamics

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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. Internal Energy of a Classical ideal gas. - PowerPoint PPT Presentation
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Page 1: Thermodynamics

Thermodynamics

Page 2: 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

Page 3: 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) kTEK

23

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

kTEK25

pVkTNU23

23

Page 4: Thermodynamics

Internal Energy of a Gas

pVkTNU23

23

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

Page 5: Thermodynamics

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

Page 6: Thermodynamics

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)

Page 7: Thermodynamics

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)

Page 8: Thermodynamics

Total Work Done

PdVdW

f

i

V

V

PdVW

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

Page 9: Thermodynamics

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.

Page 10: Thermodynamics

Different Thermodynamic Paths

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

Page 11: Thermodynamics

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

Page 12: Thermodynamics

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.

Page 13: Thermodynamics

-- 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

orU = Q - Wby

State Function Process Functions

Page 14: Thermodynamics

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 : positivesystem addedheat : positive

byto

WQ

WQU

Page 15: Thermodynamics

The First Law of ThermodynamicsbydWdQdE 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

Efficiency of the engine (e) ratio of the work to the heat absorbed

= = 1-

Page 16: Thermodynamics

The Carnot Cycle

Page 17: Thermodynamics

Carnot Engine

• Carnot cycle run in forward direction along abcda- Carnot Engine

ab

cd Q2w

Q1

Page 18: Thermodynamics

Carnot Refrigerator

• Carnot cycle run in reverse direction along adcba

ab

cd Q2w

Q2+w

Page 19: Thermodynamics

In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process.

Changes are infinitesimally small in a reversible process.

= 1- = 1-

Efficiency of heat engine (e) in terms of absolute temperature

Page 20: Thermodynamics

Carnot’s TheoremThe efficiency of any heat engine operating between two heat reservoirs of high and low temperatures is never greater than the efficiency of a Carnot engine; the efficiency of any reversible engine equals the efficiency of a Carnot engine.

Page 21: Thermodynamics

• Irreversible processes cannot be undone by exactly reversing the change to the system.

• All Spontaneous processes are irreversible.• All Real processes are irreversible.

Page 22: Thermodynamics

Entropy

• Entropy (S) is a term coined by Rudolph Clausius in the 19th century.

• Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, Q

T

Page 23: Thermodynamics

• Entropy can be thought of as a measure of the randomness of a system.

• It is related to the various modes of motion in molecules.

Page 24: Thermodynamics

Second Law of Thermodynamics

The second law of thermodynamics: The entropy of the universe does not change for reversible processes

and increases for spontaneous processes.Reversible (ideal):

Irreversible (real, spontaneous):

Page 25: Thermodynamics

Third Law of Thermodynamics

The third law of thermodynamics: the entropy of a system at absolute zero is zero

.


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