Download Revision Part 3 (ppt)

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Nanogenerator wikipedia , lookup

Thermal runaway wikipedia , lookup

Electric charge wikipedia , lookup

Ohm's law wikipedia , lookup

Lumped element model wikipedia , lookup

Transcript
Revision :
Thermodynamics
Formula sheet
Formula sheet
Formula sheet
Thermodynamics key facts (1/9)
β€’ Heat is an energy [measured in 𝐽] which flows
from high to low temperature
β€’ When two bodies are in thermal equilibrium
they have the same temperature
β€’ The S.I. unit of temperature is Kelvin (𝐾).
This is related to degrees Celsius ℃ by
𝑇 𝐾 = 𝑇 ℃ + 273
β€’
Temperature difference Δ𝑇 is the same in both units
Thermodynamics key facts (2/9)
β€’ Heat energy needed to raise a temperature
β€’ The specific heat capacity 𝑐 determines the
energy 𝑄 needed to raise the temperature of
mass π‘š of a substance by βˆ†π‘‡
𝑄 = π‘š 𝑐 βˆ†π‘‡
β€’
Units of 𝑐 will be 𝐽 π‘˜π‘”βˆ’1 𝐾 βˆ’1
Thermodynamics key facts (3/9)
β€’ Heat energy needed to change phase
β€’ The latent heat 𝐿 determines the energy 𝑄
needed to change the phase of a mass π‘š
𝑄=π‘šπΏ
β€’
Units of 𝐿 will be 𝐽 π‘˜π‘”βˆ’1 - can be fusion or vaporization
β€’
This energy is either absorbed (solid β†’ liquid β†’ gas) or
released (gas β†’ liquid β†’ solid)
β€’
A phase change takes place at constant temperature
Thermodynamics key facts (4/9)
β€’ Conduction is heat energy transfer by direct
molecular contact
Heat transfer
𝑇 + βˆ†π‘‡
Power =
𝑇
Area 𝐴
Thickness βˆ†π‘₯
βˆ†π‘„
βˆ†π‘‘
=πœ…π΄
Δ𝑇
Ξ”π‘₯
πœ… = thermal conductivity
Thermodynamics key facts (5/9)
β€’ Convection is heat energy transfer by the bulk
flow of material
Thermodynamics key facts (6/9)
β€’ Radiation is heat energy transfer by emission
of electromagnetic radiation
Power =
βˆ†π‘„
βˆ†π‘‘
= 𝜎 𝐴 𝑇4
𝜎 = Stefan-Boltzmann constant,
𝐴 = surface area of emitter,
𝑇 = temperature of emitter
(assumes emissivity=1)
Thermodynamics key facts (7/9)
β€’ Ideal gas law
β€’ 1st form : 𝑃 𝑉 = 𝑁 π‘˜π΅ 𝑇
β€’
𝑃 = Pressure, 𝑉 = Volume,
𝑁 = number of molecules,
π‘˜π΅ = Boltzmann’s constant,
𝑇 = temperature [in K]
β€’ 2nd form : 𝑃 𝑉 = 𝑛 𝑅 𝑇
β€’
𝑛 = number of moles, 𝑅 =
gas constant
Thermodynamics key facts (8/9)
β€’ Kinetic theory of ideal gas
β€’ Pressure is due to
molecular collisions
β€’ Average kinetic energy of
molecules depends on
temperature
1
2
π‘šπ‘£
2
= 32π‘˜π΅ 𝑇
π‘š = mass of molecule,
𝑣 2 = average square speed,
𝑇 = temperature
Thermodynamics key facts (9/9)
β€’ Thermal expansion
β€’ Materials expand due to temperature rise βˆ†π‘‡
β€’ Length 𝐿 increases by βˆ†πΏ = Ξ± 𝐿 βˆ†π‘‡ where 𝛼 =
coefficient of linear expansion
β€’ Volume V increases by βˆ†π‘‰ = 𝛽 𝑉 βˆ†π‘‡ where
𝛽 = coefficient of volume expansion
Practice exam questions: Section A
𝐾𝐸 = 12π‘šπ‘£ 2 = 32π‘˜π΅ 𝑇
Option C
𝑄 = π‘š 𝑐 βˆ†π‘‡
𝑄 = π‘šπ‘€π‘Žπ‘‘π‘’π‘Ÿ π‘π‘€π‘Žπ‘‘π‘’π‘Ÿ βˆ†π‘‡π‘€π‘Žπ‘‘π‘’π‘Ÿ = 1 × 4186 × 5 = 20930 𝐽
𝑄
20930
βˆ†π‘‡π΄π‘™ =
=
= 12 𝐾
π‘šπ΄π‘™ 𝑐𝐴𝑙 2 × 900
Option B
Practice exam questions: Section A
Heat energy loss is by conduction – option B
Practice exam questions: Section A
Δ𝐿
= 𝛼 Δ𝑇
𝐿
Fractional expansion is
the same – option A
Reflects radiation – option A
Practice exam questions: Section B
𝑄 = π‘š 𝑐 βˆ†π‘‡ = 2.2 × 900 × 18 = 3.6 × 104 𝐽
Practice exam questions: Section B
Stefan-Boltzmann law: 𝑃 = 𝜎 𝐴 𝑇 4
Re-arranging: 𝐴 =
𝑃
𝜎 𝑇4
=
70
5.67×10βˆ’8 × 2800 4
= 2.0 × 10βˆ’5 π‘š2
Practice exam questions: Section B
Ideal gas law (using moles): 𝑃𝑉 = 𝑛𝑅𝑇
𝑉 = 2.2 π‘™π‘–π‘‘π‘Ÿπ‘’π‘  = 2.2 × 10βˆ’3 π‘š3
𝑇 = βˆ’130 + 273 = 143 𝐾
𝑛𝑅𝑇 2.9 × 8.31 × 143
6
𝑃=
=
=
1.6
×
10
π‘ƒπ‘Ž
βˆ’3
𝑉
2.2 × 10
Practice exam questions: Section C
𝑄 = π‘šπ‘€π‘Žπ‘‘π‘’π‘Ÿ π‘π‘€π‘Žπ‘‘π‘’π‘Ÿ βˆ†π‘‡ + π‘šπ‘π‘œπ‘π‘π‘’π‘Ÿ π‘π‘π‘œπ‘π‘π‘’π‘Ÿ βˆ†π‘‡
𝑄 = 0.35 × 4186 × 3.3 + 0.25 × 387 × 3.3 = 5150 𝐽
𝑄 = π‘šπ‘–π‘π‘’ 𝐿𝑓 + π‘šπ‘–π‘π‘’ π‘π‘€π‘Žπ‘‘π‘’π‘Ÿ βˆ†π‘‡ = 5150 𝐽
5150 βˆ’ (0.012 × 4186 × 21.7)
𝐿𝑓 =
= 3.39 × 105 𝐽/π‘˜π‘”
0.012
Practice exam questions: Section C
Heat loss rate = πœ… 𝐴
Δ𝑇
βˆ†π‘₯
= 0.80 × 5.0 ×
13
2.4×10βˆ’3
= 2.2 × 104 π‘Š
Practice exam questions: Section C
Atomic mass = 4.0 × 1.66 × 10βˆ’27 = 6.64 × 10βˆ’27 π‘˜π‘”
1
2
π‘šπ‘£
π‘Ÿπ‘šπ‘ 
2
π‘£π‘Ÿπ‘šπ‘  =
3π‘˜π΅ 𝑇
=
π‘š
= 32π‘˜π΅ 𝑇
𝑇 = 127 + 273 = 400 𝐾
3 × 1.38 × 10βˆ’23 × 400
3
βˆ’1
=
1.58
×
10
π‘š
𝑠
6.64 × 10βˆ’27
Practice exam questions: Section C
𝑄 = π‘ƒπ‘œπ‘€π‘’π‘Ÿ × π‘‡π‘–π‘šπ‘’ = 2.2 × 103 × 5.9 × 60 = 7.8 × 105 𝐽
𝑄 = π‘š 𝑐 βˆ†π‘‡
𝑄
7.8 × 105
π‘š=
=
= 2.4 π‘˜π‘”
𝑐 βˆ†π‘‡ 4186 × 79
Next steps
β€’ Make sure you are comfortable with unit
conversions
β€’ Review the thermodynamics key facts
β€’ Familiarize yourself with the thermodynamics
section of the formula sheet
β€’ Try questions from the sample exam papers on
Blackboard and/or the textbook
Revision :
Electricity
Formula sheet
Formula sheet
Electricity key facts (1/9)
β€’ Electric charge 𝑄 is an intrinsic property of
the particles that make up matter, and can be
positive (e.g. proton) or negative (e.g. electron)
β€’ The S.I. unit of charge is Coulombs (𝐢)
β€’ The elementary charge (on a proton or
electron) is ± 1.6 × 10βˆ’19 𝐢
β€’ Electric current 𝐼 is the rate of flow of charge
βˆ†π‘„
𝐼=
βˆ†π‘‘
𝐼 is measured in Amperes (𝐴)
Electricity key facts (2/9)
β€’ Coulomb’s Law gives the force felt by two
charges 𝑄1 and 𝑄2 separated by distance π‘Ÿ
𝐹
𝑄1
π‘˜ 𝑄1 𝑄2
𝐹=
π‘Ÿ2
π‘Ÿ
𝐹
𝑄2
π‘˜ = 9 × 109 𝑁 π‘š2 𝐢 βˆ’2
β€’ Like charges repel, opposite charges attract
Electricity key facts (2/9)
β€’ Superposition principle for Coulomb’s Law :
if there are multiple charges, the forces
from individual charges sum like vectors
+ve
𝐹1
+ve
+ve
𝐹2
πΉπ‘‘π‘œπ‘‘π‘Žπ‘™ = 𝐹1 + 𝐹2
Electricity key facts (3/9)
β€’ The electric field at a point is the force a unit
charge (π‘ž = 1 𝐢) would experience there
𝐹
𝐸=
π‘ž
𝐹=π‘žπΈ
β€’ Can be represented by electric field lines
Positive charge feels force
along electric field line
Negative charge feels force
the other way
Electricity key facts (4/9)
β€’ The electric potential difference Δ𝑉 [in volts] is
the work needed to move unit charge (π‘ž = 1 𝐢)
between 2 points
Work done = Potential Energy difference = π‘ž Δ𝑉
β€’
Electric field is the potential gradient :
𝐸=
βˆ†π‘‰
βˆ’
βˆ†π‘₯
If capacitor with plate separation
𝐷 is connected to battery with
potential 𝑉, then 𝐸 = 𝑉/𝐷
Electricity key facts (5/9)
β€’ Basic circuit principles : current 𝐼 is driven by
a potential difference 𝑉
Same current flows
through all components
of a series circuit
Same voltage is dropped
over all components of a
parallel circuit
Electricity key facts (6/9)
β€’ Ohm’s Law determines the current flowing
through a resistance 𝑅
𝑉
𝐼=
𝑅
β€’ Resistance is measured in Ohms (Ξ©)
𝑉=𝐼𝑅
Electricity key facts (6/9)
β€’ Resistances may be combined in series or
parallel
𝑅1
𝑅2
π‘…π‘‘π‘œπ‘‘π‘Žπ‘™ = 𝑅1 + 𝑅2
[R increases]
𝑅1
1
𝑅2
π‘…π‘‘π‘œπ‘‘π‘Žπ‘™
1
1
=
+
𝑅1 𝑅2
[R decreases]
Electricity key facts (7/9)
β€’ Electrical energy is dissipated as heat by a resistor
β€’ Electrical Power 𝑃 = 𝐼 𝑉 = 𝐼2 𝑅 =
𝑉2
[unit is W]
𝑅
Electricity key facts (8/9)
β€’ A capacitor is a device to store charge. Its
capacitance 𝐢 measures the amount of charge 𝑄
that can be stored for given potential difference 𝑉
+𝑄
βˆ’π‘„
𝑄
𝐢=
𝑉
𝑄=𝐢𝑉
β€’ Capacitance is measured in
Farads (𝐹)
𝑉
β€’ Capacitors may be combined in
series or parallel [see lectures]
Electricity key facts (9/9)
β€’ General circuits may be analysed using
Kirchoff’s rules
Kirchoff’s junction rule :
the sum of currents at
any junction is zero
𝐼1
𝐼1 + 𝐼2 βˆ’ 𝐼3 = 0
𝐼2
𝐼3
β€’
Signs are different for inward/outward current
β€’
This rule arises from conservation of charge
Electricity key facts (9/9)
β€’ General circuits may be analysed using
Kirchoff’s rules
Kirchoff’s loop rule : the
sum of voltage changes
around a closed loop is zero
4Ξ©
𝐼1
9𝑉
2Ξ©
𝐼2
9 βˆ’ 4 𝐼1 βˆ’ 2 𝐼2 = 0
β€’
Battery adds potential 𝑉, resistors subtract potential 𝐼𝑅
β€’
This rule arises from conservation of energy
Practice exam questions: Section A
Coulomb’s Law: 𝐹 =
π‘˜ 𝑄1 𝑄2
π‘Ÿ2
1
4
Double π‘Ÿ β†’ 𝐹 decreases by – option A
Current is the same β†’ 𝑉 = 𝐼 𝑅 β†’ smaller voltage across smaller 𝑅 β†’ option B
Practice exam questions: Section A
Decreases – option B
Practice exam questions: Section B
π‘Š = π‘ž βˆ†π‘‰π΄π΅
π‘Š
45
βˆ†π‘‰π΄π΅ =
=
= 3000 𝑉
βˆ’3
π‘ž
15 × 10
Practice exam questions: Section B
Ohm’s Law: 𝐼 =
𝑉
𝑅
=
110
47×103
= 2.3 × 10βˆ’3 𝐴
Practice exam questions: Section B
1
π‘…π‘‘π‘œπ‘‘π‘Žπ‘™
1
1
=
+
𝑅1 𝑅2
1
1
1
=
+
45 56 𝑅2
𝑅2 = 230 π‘˜Ξ©
Practice exam questions: Section C
𝐼1 + 𝐼2 βˆ’ 𝐼3 = 0
10 βˆ’ 6𝐼1 βˆ’ 2𝐼3 = 0
5 βˆ’ 3𝐼1 βˆ’ 𝐼3 = 0
βˆ’4𝐼2 βˆ’ 14 + 6𝐼1 βˆ’ 10 = 0
βˆ’2𝐼2 βˆ’ 12 + 3𝐼1 = 0
Practice exam questions: Section C
𝑉𝑏𝑐 = βˆ’10 + 𝑉6Ξ© = 2 𝑉 β†’ 𝑉6Ξ© = 12 𝑉
𝑉 12
𝐼1 = =
=2𝐴
𝑅
6
From before: 5 βˆ’ 3𝐼1 βˆ’ 𝐼3 = 0
𝐼3 = 5 βˆ’ 3𝐼1 = 5 βˆ’ 3 × 2 = βˆ’1 𝐴
Practice exam questions: Section C
From before:βˆ’2𝐼2 βˆ’ 12 + 3𝐼1 = 0
3𝐼1 βˆ’ 12 βˆ’6
𝐼2 =
=
= βˆ’3 𝐴
2
2
𝑃 = 𝐼3 2 𝑅 = βˆ’1
2
×2=2π‘Š
Practice exam questions: Section C
Combine the 2Ξ©, 4Ξ©, 6Ξ© resistors in parallel
1
1 1 1
= + + β†’ π‘…π‘π‘Žπ‘Ÿπ‘Žπ‘™π‘™π‘’π‘™ = 1.1 Ξ©
π‘…π‘π‘Žπ‘Ÿπ‘Žπ‘™π‘™π‘’π‘™ 2 4 6
Combine the 1Ξ©, 1.1Ξ© resistors in series π‘…π‘‘π‘œπ‘‘π‘Žπ‘™ = 2.1 Ξ©
Ohm’s Law: 𝐼 =
𝑉
π‘…π‘‘π‘œπ‘‘π‘Žπ‘™
=
6
2.1
= 2.9 𝐴
Practice exam questions: Section C
Voltage across parallel combination =
1.1
2.1
𝑉 3.1
𝐼= =
= 0.52 𝐴
𝑅
6
× 6 𝑉 = 3.1 𝑉
Final words
β€’ Thanks to all students for their efforts in the
Introduction to Physics course
β€’ Please fill in feedback surveys!
β€’ Good luck in the upcoming exams!