Heat, Work, and the First Law of Thermodynamics 298 summer... · • A thermodynamic system is any...

1Prof. Sergio B. MendesSummer 2018

Chapter 18 of Essential University Physics, Richard Wolfson, 3rd Edition

Heat, Work, and the First Law of Thermodynamics

Different ways to increase the internal energy of system:

Joule’s apparatus to determine the conversion of mechanical work into

changes of internal energy:

• A thermodynamic system is any collection of objects that may exchange energy (work and/or heat) with its surroundings.

• In a thermodynamic process, changes occur in the state of the system.

It’s all about the system !!

First Law of Thermodynamics:

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑄𝑄 + 𝑊𝑊

𝑄𝑄: heat transferred to the system

𝑊𝑊: work done on the system

Be careful with the signs:

Q is positive when heat flows into the system.

W is positive when work is done on the system.

A state in which the macroscopic properties

(p, V, and T)

no longer change with time, if the system is thermally and mechanically isolated.

Thermodynamic Equilibrium:

• There is a precise relation between p, V, and T (phase diagram).

• For example, given p and V, T can be determined exactly and uniquely.

If the System is in Thermodynamic Equilibrium:

• Then just two physical properties (e.g., p and V) are sufficient to characterize the state of the system in thermodynamic equilibrium.

𝑄𝑄: heat transferred to the system

𝑊𝑊: work done on the system

Thermodynamic Processes

The system is no longer thermally and mechanically isolated.

How can we describe the system as it

changes ?

A process in which the system is always in thermodynamic equilibrium. Its evolution from one

state to another is described by a continuous sequence of points in its pV diagram.

The Quasi-Static Process:

Quasi-static processes are reversible !!

Under Those Conditions:

Work Done on the System:

𝑑𝑑𝑊𝑊 = 𝐹𝐹 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝐴𝐴 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝑑𝑑𝑑𝑑

𝑊𝑊 = −�𝑉𝑉1

𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑

As an Example of Reversible Thermodynamic Processes,

we will use the Ideal Gas.

Because we have a simple relation between p, V, and T.

𝑝𝑝 𝑑𝑑 = 𝑛𝑛 𝑅𝑅 𝑇𝑇

The Isothermal Process

𝑊𝑊 = −�𝑉𝑉1

𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑 = −�

𝑉𝑉1

𝑉𝑉2 𝑛𝑛 𝑅𝑅 𝑇𝑇𝑑𝑑

𝑑𝑑𝑑𝑑 = −𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1

Internal Energyof the Ideal Gas

𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑁𝑁 �𝐾𝐾

�𝐾𝐾 =32𝑘𝑘 𝑇𝑇

= 𝑁𝑁32𝑘𝑘 𝑇𝑇

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇

= 𝑛𝑛32𝑅𝑅 𝑇𝑇

Back to the Isothermal Process

∆𝑇𝑇 = 0

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 0

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑄𝑄 + 𝑊𝑊 = 0

𝑄𝑄 = −𝑊𝑊 = 𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1

Reversible Thermodynamic Processes of the Ideal Gas

𝑄𝑄 ≡ 𝑛𝑛 𝐶𝐶𝑣𝑣 ∆𝑇𝑇

−𝑊𝑊 = 𝑝𝑝 ∆𝑑𝑑 = 𝑛𝑛 𝑅𝑅 ∆𝑇𝑇

𝛾𝛾 ≡𝐶𝐶𝑝𝑝𝐶𝐶𝑣𝑣= ∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖

= 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇

𝑄𝑄 ≡ 𝑛𝑛 𝐶𝐶𝑝𝑝 ∆𝑇𝑇

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛 𝐶𝐶𝑣𝑣 ∆𝑇𝑇

Specific Heatof the Ideal Gas

∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇

= 𝑛𝑛 𝐶𝐶𝑣𝑣 ∆𝑇𝑇

𝐶𝐶𝑣𝑣 =32𝑅𝑅 𝛾𝛾 ≡

𝐶𝐶𝑝𝑝𝐶𝐶𝑣𝑣

𝐶𝐶𝑝𝑝 = 𝐶𝐶𝑣𝑣 + 𝑅𝑅 =52𝑅𝑅 =

Kinetic Theory of the Ideal Gas

For analysis we assume:

Gas pressure arises from the average force the particles exert when they

collide with the container walls.

• N identical particles of mass m and no internal structure

• Collisions with the wall of the container are elastic

• Molecular motion is random

• No intermolecular forces and molecules only have kinetic energy

The ideal-gas law follows by assuming that a gas consists of particles that obey Newton's laws.

Monatomic Molecule: He, Ne, Ar, etc

• Translational motion in 3D along x, y, z

• 3 degrees of freedom

• Each degree of freedom contributes with 12𝑘𝑘 𝑇𝑇 to the

internal energy: 𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛 32𝑅𝑅 𝑇𝑇

�𝐾𝐾 =32𝑘𝑘 𝑇𝑇

𝐶𝐶𝑣𝑣 =32𝑅𝑅 𝛾𝛾 =

53𝐶𝐶𝑝𝑝 =

52𝑅𝑅

Diatomic Molecules: H2, O2, N2, etc.

• Translational motion in 3D along x, y, z

• Rotational motion along two axis

• 5 degrees of freedom

• Each degree of freedom contributes with 12𝑘𝑘 𝑇𝑇 to the

internal energy: 𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛 52𝑅𝑅 𝑇𝑇

𝐶𝐶𝑣𝑣 =52𝑅𝑅 𝛾𝛾 =

75𝐶𝐶𝑝𝑝 =

72𝑅𝑅

Heat, Work, and the First Law of Thermodynamics 298 summer... · • A thermodynamic system is any...

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