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1Prof. Sergio B. MendesSummer 2018
Chapter 18 of Essential University Physics, Richard Wolfson, 3rd Edition
Heat, Work, and the First Law of Thermodynamics
2Prof. Sergio B. MendesSummer 2018
Different ways to increase the internal energy of system:
3Prof. Sergio B. MendesSummer 2018
Joule’s apparatus to determine the conversion of mechanical work into
changes of internal energy:
4Prof. Sergio B. MendesSummer 2018
• 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 !!
5Prof. Sergio B. MendesSummer 2018
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.
6Prof. Sergio B. MendesSummer 2018
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:
7Prof. Sergio B. MendesSummer 2018
• 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.
8Prof. Sergio B. MendesSummer 2018
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 ?
9Prof. Sergio B. MendesSummer 2018
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 !!
10Prof. Sergio B. MendesSummer 2018
Under Those Conditions:
11Prof. Sergio B. MendesSummer 2018
Work Done on the System:
𝑑𝑑𝑊𝑊 = 𝐹𝐹 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝐴𝐴 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝑑𝑑𝑑𝑑
𝑊𝑊 = −�𝑉𝑉1
𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑
12Prof. Sergio B. MendesSummer 2018
As an Example of Reversible Thermodynamic Processes,
we will use the Ideal Gas.
Why ?
Because we have a simple relation between p, V, and T.
𝑝𝑝 𝑑𝑑 = 𝑛𝑛 𝑅𝑅 𝑇𝑇
13Prof. Sergio B. MendesSummer 2018
The Isothermal Process
𝑊𝑊 = −�𝑉𝑉1
𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑 = −�
𝑉𝑉1
𝑉𝑉2 𝑛𝑛 𝑅𝑅 𝑇𝑇𝑑𝑑
𝑑𝑑𝑑𝑑 = −𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1
14Prof. Sergio B. MendesSummer 2018
Internal Energyof the Ideal Gas
𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑁𝑁 �𝐾𝐾
�𝐾𝐾 =32𝑘𝑘 𝑇𝑇
= 𝑁𝑁32𝑘𝑘 𝑇𝑇
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇
= 𝑛𝑛32𝑅𝑅 𝑇𝑇
15Prof. Sergio B. MendesSummer 2018
Back to the Isothermal Process
∆𝑇𝑇 = 0
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 0
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑄𝑄 + 𝑊𝑊 = 0
𝑄𝑄 = −𝑊𝑊 = 𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1
16Prof. Sergio B. MendesSummer 2018
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
17Prof. Sergio B. MendesSummer 2018
Specific Heatof the Ideal Gas
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇
= 𝑛𝑛 𝐶𝐶𝑣𝑣 ∆𝑇𝑇
𝐶𝐶𝑣𝑣 =32𝑅𝑅 𝛾𝛾 ≡
𝐶𝐶𝑝𝑝𝐶𝐶𝑣𝑣
𝐶𝐶𝑝𝑝 = 𝐶𝐶𝑣𝑣 + 𝑅𝑅 =52𝑅𝑅 =
53
18Prof. Sergio B. MendesSummer 2018
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.
19Prof. Sergio B. MendesSummer 2018
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
20Prof. Sergio B. MendesSummer 2018
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