11: Engineering Physics Flashcards
(65 cards)
1
Q
First Law of Thermodynamics (4)
A
- Q = ΔU + W
- Q is energy transferred to the system by heating
- ΔU is the increase in internal energy
- W is work done by the system
2
Q
Ideal Gas Equation
A
p V = n R T
3
Q
Isothermal Changes (4)
A
- Where the temperature of the system is constant
- The gas’s absolute temperature determines its internal energy
- So ΔU = 0, meaning Q = W
- Hence, supplying heat energy to the system results in an equivalent amount of work being done by the gas so its volume increasing
4
Q
Isothermal Change Equation
A
p V = constant
5
Q
Adiabatic Changes (3)
A
- Where no heat is transferred in or out of the system
- So Q = 0 meaning ΔU = -W
- Hence, any change in the internal energy of the system is caused by work done by/on the system
6
Q
Adiabatic Change Equation
A
p V^γ = constant
7
Q
Constant Pressure Change Equation
A
V / T = constant
8
Q
Constant Volume Changes (3)
A
- If volume is constant, no work is done by/on the system
- So W = 0 meaning Q = ΔU
- Hence, all heat energy transferred to the system goes into increasing its internal energy
9
Q
Constant Volume Change Equation
A
p / T = constant
10
Q
p-V Diagrams for Isothermal Changes (3)
A
- p-V diagram for a compression, where work is done on the system:
Textbook p539 Figure 2 - p-V diagram for an expansion, where work is done by the system:
Textbook p539 Figure 2 - The higher the temperature of the process, the further from the origin the p-V diagram is
11
Q
p-V Diagrams for Adiabatic Changes (3)
A
- The p-V curves for adiabatic processes have a steeper gradient than isothermal processes
- More work is done to compress gas adiabatically than isothermally:
Textbook p540 Figure 4 - The gas does less work if it expands adiabatically instead of isothermally
Textbook p541 Figure 5
12
Q
p-V Diagram for Constant Volume Changes (3)
A
- p-V diagrams for changes with constant volume are straight vertical lines
- No work is done as volume doesn’t change and there is no area under the line
- If a system is heated at constant volume, its pressure will increase:
Textbook p541 Figure 6
13
Q
p-V Diagram for Constant Pressure Changes (3)
A
- p-V diagrams for constant pressure changes are straight horizontal lines
- The work done is the area of the rectangle under the graph – W = p ΔV
- Textbook p541 Figure 7
14
Q
Work Done =
A
Area below the graph
15
Q
Work Done per Cycle =
A
Area of loop
16
Q
Four-Stroke Petrol Engine Cycle (4)
A
- Induction
- Compression
- Expansion
- Exhaust
17
Q
Induction (3)
A
- The piston moves down, increasing the volume of the gas (air-fuel mix) as the inlet valve is open
- The pressure of the gas remains constant just below atmospheric pressure
- Indication diagram: Textbook p544 Figure 1
18
Q
Compression (5)
A
- The inlet valve is closed and the piston moves up the cylinder
- This does work on the gas, increasing the pressure
- Just before the piston is at the end of this stroke, the spark plug creates a spark, igniting the gas
- The temperature and pressure increase at almost constant volume
- Indication diagram: Textbook p544 Figure 3
19
Q
Expansion (4)
A
- The hot gas expands and does work on the piston, pushing it down
- The work done by the gas is greater than the work done to compress it as it is now at a higher temperature
- Just before the piston is at the end of this stroke, the exhaust valve opens, reducing the pressure
- Indication diagram: Textbook p545 Figure 4
20
Q
Exhaust (3)
A
- The piston moves up the cylinder and the burnt gas leaves through the exhaust valve
- The pressure remains almost constant
- Indication diagram: Textbook p545 Figure 5
21
Q
Four-Stroke Diesel Engine Cycle (5)
A
- In the induction stroke, only air is pulled into the cylinder
- Diesel engines don’t have a spark plug, so in the compression stroke, the air is compressed until its temperature is high enough to ignite the fuel
- Just before the end of the stroke, diesel is sprayed into the cylinder through a fuel injector and ignites
- The expansion and exhaust strokes are the same as a petrol engine
- The indicator diagram has a flatter peak at the start of the expansion stroke, showing the point where fuel is injected and heats up to combustion temperature:
Textbook p545 Figure 7
22
Q
Assumption of Theoretical Cycles (5)
A
- The same gas is taken continuously around the cycle
- The gas is pure air with an adiabatic constant γ = 1.4
- Pressure and temperature changes can be instantaneous
- The heat source is external
- The engine is frictionless
23
Q
Petrol Engine Cycle Theoretical Diagram (5)
A
- A: The gas is compressed adiabatically
- B: Heat is supplied at constant volume
- C: The gas cools adiabatically
- D: The system cools at constant volume
- Textbook p546 Figure 8
24
Q
Diesel Engine Cycle Theoretical Diagram (5)
A
- A: The gas is compressed adiabatically
- B: Heat is supplied at constant pressure
- C: The gas cools adiabatically
- D: The system cools at constant volume
- Textbook p546 Figure 10
25
Comparison of Theoretical and Real Diagrams (7)
* Curved corners: because valves take finite time to open and close
* No constant volume process: because piston would have to stop
* Compression and expansion not adiabatic curves: because energy is lost by heat transfer
* The cycle is open because engine needs to
draw in air and expel exhaust
* Heating not at constant pressure: because fuel injection and combustion cannot be exactly controlled
* Area of diagram is less because energy is lost by heat
transfer and incomplete combustion
* Pressure not as high because incomplete combustion
26
Indicated Power =
(Area of p–V loop) x (no. of cycles per second) x (no. of cylinders)
27
Output or Brake Power Equation
P = T ω
28
Friction Power =
Indicated power - brake power
29
Input Power =
Calorific value x fuel flow rate
30
Engine Efficiency (5)
- Mechanical efficiency is affected by the amount of energy lost through moving parts
- Mechanical efficiency = brake power / indicated power
- Thermal efficiency describes how well heat energy is transferred into work
- Thermal efficiency = indicated power / input power
- Overall efficiency = brake power / input power
31
Impossibility of Engine Working only by First Law (4)
- No engine can transfer all the heat energy it is supplied into useful work
- Some heat ends up increasing the temperature of the engine
- If the engine temperature reaches that of the heat source, then no heat flows and no work is done
- So, engines cannot work by only the first law as Q and W would both be 0
32
Second Law of Thermodynamics
The need for a heat engine to operate between a source and a sink
33
Diagram of Heat Engine Operating between Heat Source & Heat Sink
Textbook p552 Figure 1
34
Heat Engine Efficiency =
W / Q_H = (Q_H - Q_C) / Q_H
35
Heat Engine Maximum Theoretical Efficiency =
(T_H - T_C) / T_H
36
Reason for Lower Efficiencies of Practical Engines
There is usually a lot of waste heat, which is transferred to the surround area and lost
37
Combined Heat & Power Schemes
They use waste heat to heat houses and supply heat to businesses nearby as well as generate electricity to use and supply to the national grid
38
Refrigerators (4)
- The cold space is inside the refrigerator and the hot space is the refrigerator's surroundings
- A refrigerator extracts heat energy from the cold space
- Work is done to transfer heat energy via pipes on the back of the appliance
- Refrigerators keep enclosed spaces cool so they can keep perishable food fresh
39
Heat Pumps (3)
- The cold space is outdoors and the hot space is inside a house
- A heat pump pumps heat into the hot space
- They are used to heat rooms and water in homes
40
Reversed Heat Engine Diagram
Textbook p555 Figure 1
41
Coefficient of Performance
The amount of heat energy transferred per unit of work done
42
Refrigerator Coefficient of Performance (3)
- It's the heat removed from the cold space, that's important for a refrigerator
- COP_ref = Q_C / W = Q_C / (Q_H - Q_C)
- Maximum theoretical COP_ref = T_C / (T_H - T_C)
43
Heat Pump Coefficient of Performance (3)
- It's the heat transferred to the hot space, that's important for a heat pump
- COP_hp = Q_H / W = Q_H / (Q_H - Q_C)
- Maximum theoretical COP_hp = T_H / (T_H - T_C)
44
Moment of Inertia
A measure of how much an object resists a change to its rotational speed
45
Moment of Inertia for a Point Mass
I = m r²
46
Moment of Inertia for an Extended Object
I = Σ m r²
47
Factors Affecting Moment of Inertia (2)
* The magnitude of the object's mass
* The distribution of the object's mass about its centre of rotation
48
Angular Kinetic Energy Equation
Eₖ = 1/2 I ω²
49
Factors Affecting Energy Storage Capacity of a Flywheel (3)
* Increase its mass to increase its moment of inertia and so kinetic energy stored
* Increase its angular speed to increase its kinetic energy stored
* Use a wheel with spokes or a heavier rim so more mass is concentrated further from the axis of rotation, increasing its moment of inertia and kinetic energy stored
50
Flywheel
A heavy wheel, which has a high moment of inertia in order to resist changes to its rotational motion
51
Uses of Flywheels in Machines (3)
* Flywheels are charged as they are spun, turning input torque into rotational kinetic energy. If it keeps spinning at the same rate, it stores the energy for later use
* Just enough power is continuously input to overcome frictional torque, keeping the flywheel fully charged
* When extra energy is needed, the flywheel decelerates, transferring some of its kinetic energy to another part of the machine
52
Uses of Flywheels for Smoothing Torque & Speed (4)
* Flywheels are used in machines to smooth engine and load (torque due to resistance forces) torque
* In systems where the power supplied can vary, flywheels keep the angular velocity of rotating components constant. It uses each spurt of power to charge and delivers the energy smoothly
* In systems where the force to exert can vary, flywheels are used. If the load torque is too high, the flywheel decelerates, releasing extra energy
* If the engine torque is greater than the load torque, the flywheel charges by accelerating to store the spare energy
53
Angular Displacement
The angle through which a point has been rotated
54
Angular Velocity
The angle a point rotates through per unit time
55
Angular Speed
The magnitude of angular velocity
56
Angular Acceleration
The rate of change of angular velocity
57
Angular Velocity Equation
ω = Δθ/Δt
58
Angular Acceleration Equation
α = Δω/Δt
59
Torque Equations
* T = F r
* T = I α
60
Angular Momentum Equation
angular momentum = I ω
61
Conservation of Angular Momentum
Assuming no external torques act, the total angular momentum of a system remains constant
62
Angular Impulse =
Change in angular momentum
63
Angular Impulse Equation
T Δt = Δ(I ω)
64
Rotational Dynamics Work Done Equation
W = T θ
65
Rotational Dynamics Power Equation
P = T ω
