heat, work, and the first law of thermodynamics 298 summer... · • a thermodynamic system is any...
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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
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2Prof. Sergio B. MendesSummer 2018
Different ways to increase the internal energy of system:
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3Prof. Sergio B. MendesSummer 2018
Joule’s apparatus to determine the conversion of mechanical work into
changes of internal energy:
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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 !!
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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.
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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:
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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.
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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 ?
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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 !!
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10Prof. Sergio B. MendesSummer 2018
Under Those Conditions:
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11Prof. Sergio B. MendesSummer 2018
Work Done on the System:
𝑑𝑑𝑊𝑊 = 𝐹𝐹 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝐴𝐴 𝑑𝑑𝑑𝑑 = − 𝑝𝑝 𝑑𝑑𝑑𝑑
𝑊𝑊 = −�𝑉𝑉1
𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑
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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
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13Prof. Sergio B. MendesSummer 2018
The Isothermal Process
𝑊𝑊 = −�𝑉𝑉1
𝑉𝑉2𝑝𝑝 𝑑𝑑𝑑𝑑 = −�
𝑉𝑉1
𝑉𝑉2 𝑛𝑛 𝑅𝑅 𝑇𝑇𝑑𝑑
𝑑𝑑𝑑𝑑 = −𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1
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14Prof. Sergio B. MendesSummer 2018
Internal Energyof the Ideal Gas
𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑁𝑁 �𝐾𝐾
�𝐾𝐾 =32𝑘𝑘 𝑇𝑇
= 𝑁𝑁32𝑘𝑘 𝑇𝑇
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑛𝑛32𝑅𝑅 ∆𝑇𝑇
= 𝑛𝑛32𝑅𝑅 𝑇𝑇
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15Prof. Sergio B. MendesSummer 2018
Back to the Isothermal Process
∆𝑇𝑇 = 0
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 0
∆𝐸𝐸𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑄𝑄 + 𝑊𝑊 = 0
𝑄𝑄 = −𝑊𝑊 = 𝑛𝑛 𝑅𝑅 𝑇𝑇 𝑙𝑙𝑛𝑛𝑑𝑑2𝑑𝑑1
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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
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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
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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.
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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
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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