Option C: Engineering Physics (Thermodynamics) Flashcards
In thermodynamics, what is a system?
A volume of space filled with gas.
What are the two types of system?
- Open
* Closed
What are open systems?
Those that allow gas to flow in, out or through them.
What are closed systems?
Those that don’t allow gas to enter or escape.
What does the first law of thermodynamics describe?
How energy is conserved in a system through heating, cooling and doing work.
State the first law of thermodynamics.
The heat energy supplied to the system either increase the internal energy or enables it to do work.
Give the equation for the first law of thermodynamics.
Q = ΔU + W
Where:
• Q = Heat energy transferred to the system
• ΔU = Change in internal energy
• W = Work some by the gas
In thermodynamics, what is Q?
Heat energy transferred to the system
In thermodynamics, what is ΔU?
Change in internal energy
In thermodynamics, what is W?
The work done by the system (i.e. by the gas)
What is the internal energy of a gas?
The sum of the potential and kinetic energies of all of the particles.
When heat is transferred to the system, what is the sign of Q?
Positive
When heat is transferred away from the system, what is the sign of Q?
Negative
When a gas expands, what is the sign of W?
Positive
When a gas is compressed, what is the sign of W?
Negative
A cylinder is sealed by a moveable piston. The gas in the cylinder is heated with 60J of heat to move the piston. The internal energy of the gas increases by 5J.
a) Calculate the work done by the gas to move the piston.
b) Now the piston does 60J of work on the gas to compress it. No heat is lost. Calculate the change in the internal energy of the gas.
a) W = Q - ΔU = 60 - 5 = 55J
b) ΔU = -W = 60J
What is another name for a closed system?
Non-flow process
What must be assumed when doing calculations about a gas in a closed system?
That the gas is an ideal gas.
What are some of the assumptions when working with an ideal gas?
- Internal energy ONLY depends on the temperature (i.e. potential energy is negligible)
- A change in volume means work is done
- pV = nRT applies
For an ideal gas, what does the internal energy depend on?
- Temperature (and therefore kinetic energy)
* NOT potential energy
Does the potential energy of an ideal gas in a closed system change?
No
What does a change in volume of a gas in a closed system indicate?
That work is being done.
What is the ideal gas law equation?
pV = nRT
Where: • p = Pressure (Pa) • V = Volume (m³) • n = Moles of gas (mol) • R = Gas constant (8.31J/K/mol) • T = Temperature (K)
What is the equation used in working out pressures, volumes and temperatures in a closed system undergoing a change?
p₁V₁ / T₁ = p₂V₂ / T₂
NOTE: Not given in exam
What is an isothermal change?
One that happens at constant temperature.
What quantity defines an isothermal change and why?
- ΔU = 0
* Because the internal energy only depends on the temperature, which is not changing
What can be said in terms of the first law of thermodynamics for an isothermal change?
- ΔU = 0
* So Q = W
Explain an isothermal change in terms of the first law of thermodynamics.
- The work done by a system is equal to the heat energy supplied
- The work done on the system is equal to heat energy loss of the system
What is the equation for the constant in an isothermal change?
- pV = Constant
* So: p₁V₁ = p₂V₂
What is an adiabatic change?
One where no heat is lost or gained by the system.
What quantity defines an adiabatic change and why?
- Q = 0
* Because there is no heat transfer to or away from the gas
What can be said in terms of the first law of thermodynamics for an adiabatic change?
- Q = 0
* So ΔU = -W
Explain an adiabatic change in terms of the first law of thermodynamics.
Any change in the internal energy of the system is caused by work done by/on the system.
Does an adiabatic change result in a temperature change?
Yes, since the internal energy is changing.
What is the equation for the constant in an adiabatic change?
- pV^γ = Constant
- So p₁V₁^γ = p₂V₂^γ
Where:
• γ = Adiabatic constant
What is the adiabatic constant?
- A constant used in adiabatic change calculations.
* Depends on the type of gas.
What is the adiabatic constant (γ) for a monoatomic gas?
1.67
What is the adiabatic constant (γ) for a diatomic gas?
1.40
What is the adiabatic constant (γ) for a polyatomic gas?
1.33
What is the equation for the work done to expand a gas?
W = p x ΔV
Where:
• W = Work done by the system (J)
• p = Pressure (Pa)
• ΔV = Change in volume of system (m³)
Derive W = pΔW.
- W = F x d
- F = p x A
- W = p x A x d
- W = p x ΔV
Is work done by or on a gas when it expands?
By the gas
Is work done by or on a gas when it is compressed?
On the gas.
For an isobaric change, what equation can be stated?
V₁/T₁ = V₂/T₂
This comes from pV = nRT
What is the work done when there is no change in the volume of a gas?
0
What quantity defines an isovolumetric change and why?
- W = 0
* Since no work is done if the volume is unchanging.
What can be said in terms of the first law of thermodynamics for an isovolumetric change?
- W = 0
* So Q = ΔU
Explain an isovolumetric change in terms of the first law of thermodynamics.
The internal energy of the gas increases by the heat energy transferred to it, since none is lost/gained by doing work.
What graph can be used to represent non-flow processes?
p-V diagram
When looking at the lines on a p-V diagram, what is it important to remember?
Look at the arrows to see the direction in which the change is happening.
How is the work done represented on a p-V diagram?
It is the area under the line.
Describe the p-V graph for an isothermal process.
Smooth curve between the top left and bottom right (where p₁V₁ = p₂V₂)
On a p-V diagram, which way does the arrow point on the line for an isothermal compression?
To the top left
On a p-V diagram, which way does the arrow point on the line for an isothermal expansion?
To the bottom right
What are p-V curves for isothermal processes called?
Isotherms
How does the position of an isotherm depend on the temperature?
The further the curve is from the origin, the hotter it is.
On a p-V diagram, which direction does the line have to point in order for work to be done by the gas and on the gas?
- By the gas -> To the right
* On the gas -> To the left
Describe the p-V graph for an adiabatic process.
Steep, smooth curve between the top left and bottom right
On a p-V diagram, what is the difference between the line for an adiabatic and isothermal process?
The adiabatic change is steeper.
Is more work done when compressing a gas isothermally or adiabatically? Why?
Adiabatically, because the curve is steeper, so the area under the p-V graph is larger.
Is more work done when a gas expands isothermally or adiabatically? Why?
Isothermally, because the curve is less steep, so the area under the graph is larger.
Remember to practise drawing out the p-V diagrams for an adiabatic and isothermal expansion ad compression.
See diagram pg 230 of revision guide
Describe the p-V graph for an isovolumetric process.
Straight vertical line
How can you tell from a p-V graph that an isovolumetric process involves no work being done?
- It is a straight vertical line
* So there is no area under the line, meaning no work is done
If a system is kept at a constant volume but heated between temperatures T₁ and T₂, what change will be observed?
The pressure will increase.
For an isovolumetric change on a p-V graph, what is the relative temperature at the bottom and top of the line?
- Bottom: Lower temperature
* Top: Higher temperature
No work is done in an isovolumetric change. What causes the change in pressure?
Heating or cooling
Describe the p-V graph for an isobaric process.
Straight horizontal line
On the p-V graph for an isobaric change, what is the work done?
The area under the straight horizontal line.
When is W = pΔV true?
For an isobaric change.
How is W = pΔV shown on a p-V graph?
- The work done in an isobaric change is equal to the area under the straight horizontal line.
- The height of this area is p, while the length is ΔV.
How are cyclic processes shown on a p-V graph?
They form a loop.
On a p-V diagram, how can the net work done per cycle by a cyclic process be calculated?
It is the area of the loop.
What must you remember about the work done on a p-V diagram for a cyclic process?
The area is the work done PER CYCLE.
Remember to practise labelling the p-V cycle on pg 231.
Do it.
For a cyclic process on a p-V diagram that goes clockwise, is the net work done on or by the system?
By the system.
For a cyclic process on a p-V diagram that goes anticlockwise, is the net work done on or by the system?
On the system.
Describe the structure of an internal combustion engine.
- Cylinders filled with air
- Air is trapper by tight-fitting pistons (which move up and down)
- Inlet and exhaust valves at the top of the air
- Spark plug at top of the air
In an internal combustion engine, what is a stroke?
Every time a piston moves up or down.
What graph can be used to represent non-flow processes?
p-V diagram
When looking at the lines on a p-V diagram, what is it important to remember?
Look at the arrows to see the direction in which the change is happening.
How is the work done represented on a p-V diagram?
It is the area under the line.
Describe the p-V graph for an isothermal process.
Smooth curve between the top left and bottom right (where p₁V₁ = p₂V₂)
On a p-V diagram, which way does the arrow point on the line for an isothermal compression?
To the top left
On a p-V diagram, which way does the arrow point on the line for an isothermal expansion?
To the bottom right
What are p-V curves for isothermal processes called?
Isotherms
How does the position of an isotherm depend on the temperature?
The further the curve is from the origin, the hotter it is.
On a p-V diagram, which direction does the line have to point in order for work to be done by the gas and on the gas?
- By the gas -> To the right
* On the gas -> To the left
Describe the p-V graph for an adiabatic process.
Steep, smooth curve between the top left and bottom right
On a p-V diagram, what is the difference between the line for an adiabatic and isothermal process?
The adiabatic change is steeper.
Is more work done when compressing a gas isothermally or adiabatically? Why?
Adiabatically, because the curve is steeper, so the area under the p-V graph is larger.
Is more work done when a gas expands isothermally or adiabatically? Why?
Isothermally, because the curve is less steep, so the area under the graph is larger.
Remember to practise drawing out the p-V diagrams for an adiabatic and isothermal expansion ad compression.
See diagram pg 230 of revision guide
Describe the p-V graph for an isovolumetric process.
Straight vertical line
How can you tell from a p-V graph that an isovolumetric process involves no work being done?
- It is a straight vertical line
* So there is no area under the line, meaning no work is done
If a system is kept at a constant volume but heated between temperatures T₁ and T₂, what change will be observed?
The pressure will increase.
For an isovolumetric change on a p-V graph, what is the relative temperature at the bottom and top of the line?
- Bottom: Lower temperature
* Top: Higher temperature
No work is done in an isovolumetric change. What causes the change in pressure?
Heating or cooling
Describe the p-V graph for an isobaric process.
Straight horizontal line
On the p-V graph for an isobaric change, what is the work done?
The area under the straight horizontal line.
When is W = pΔV true?
For an isobaric change.
How is W = pΔV shown on a p-V graph?
- The work done in an isobaric change is equal to the area under the straight horizontal line.
- The height of this area is p, while the length is ΔV.
How are cyclic processes shown on a p-V graph?
They form a loop.
On a p-V diagram, how can the net work done per cycle by a cyclic process be calculated?
It is the area of the loop.
What must you remember about the work done on a p-V diagram for a cyclic process?
The area is the work done PER CYCLE.
Remember to practise labelling the p-V cycle on pg 231.
Do it.
For a cyclic process on a p-V diagram that goes clockwise, is the net work done on or by the system?
By the system.
For a cyclic process on a p-V diagram that goes anticlockwise, is the net work done on or by the system?
On the system.
Describe the structure of an internal combustion engine.
- Cylinders filled with air
- Air is trapper by tight-fitting pistons (which move up and down)
- Inlet and exhaust valves at the top of the air
- Spark plug at top of the air
In an internal combustion engine, what is a stroke?
Every time a piston moves up or down.
What is a four-stroke engine?
One that burns fuel once every four strokes.
What are the 4 strokes of a four-stroke petrol engine?
1) Induction (Suck)
2) Compression (Squeeze)
3) Expansion (Bang)
4) Exhaust (Blow)
What happens in the induction stroke of a petrol engine?
- Piston starts at the top of the cylinder and moves down, increasing the volume of gas above it
- This sucks in a mixture of fuel and air through the open inlet valve
- The pressure of the gas in the cylinder remains constant just below atmospheric pressure
What happens in the compression stroke of a petrol engine?
- Inlet valve is closed
- Piston moves back up in the cylinder and does work on the gas
- Just before the piston is at the end of its stroke, the spark plug creates a spark which ignited the air-fuel mixture
- Temperature and pressure don’t suddenly increase at almost constant volume
What happens in the expansion stroke of a petrol engine?
- The hot air-fuel mixture expands and does work on the piston, moving it downwards
- The work done by the gas as it expands is more than the work done to compress the gas, as it is now at a higher temperature. There is a net output of work.
- Just before the piston is at the bottom of the stroke, the exhaust valve opens and the pressure reduces.
What happens in the exhaust stroke of a petrol engine?
- The piston moves up the cylinder, and the burnt gas leaves through the exhaust valve
- The pressure remains almost constant, just above atmospheric pressure
When is fuel injected and ignited into a petrol engine?
- The air-fuel mix is always in the system (i.e. it doesn’t have to be injected)
- It is ignited by a spark plug at the end of the compression stroke, just before the piston is at the end of its stroke.
In a petrol or diesel engine, why is more work done when the gas expands compared to when the gas is compressed?
The expansion is at a higher temperature (so the area under the line in the p-V graph is larger).
In a petrol or diesel engine, how many times per cycle does each valve open?
- Once
- The inlet valve open just at the start of the induction stroke and closes at the end of it
- The exhaust valve opens just at the start of the exhaust stroke and closes at the end of it
In a p-V diagram for a petrol or diesel engine, is the induction or exhaust stroke higher up?
Exhaust stroke
Describe the actual p-V diagram for a petrol engine.
Induction:
• Horizontal line from left to right
Compression:
• Curve to the top left, where gradient increases rapidly near the end. Sharp peak at the end.
Expansion:
• Curve to the bottom right, above the compression stroke, and of gradually shallower gradient
Exhaust:
• Horizontal line to the left, above the induction stroke
(See diagram pg 232 of revision guide)
Remember to practise writing out the stages of a petrol engine cycle.
Pg 232 of revision guide
What are some differences between how a petrol and diesel engine work?
Diesel engines are the same, except:
• Only air is pulled into the cylinder in the induction stroke (instead of an air-fuel mixture)
• Air is compressed so it reaches a temperature high enough to ignite diesel fuel before the diesel fuel is injected. No spark is used.
• The diesel engine compresses to double the petrol engine pressure.
Describe the actual p-V diagram for a diesel engine.
Induction:
• Horizontal line from left to right
Compression:
• Curve to the top left, where gradient increases more near the end
Expansion:
• Almost flat horizontal line to the right, then curve to the bottom right
Exhaust:
• Horizontal line to the left, above the induction stroke
(See diagram pg 233 of revision guide)
Where on a p-V diagram for a petrol engine is the fuel ignited?
At the bottom of the vertical part of the compression stroke
Where on a p-V diagram for a diesel engine is the fuel injected and ignited?
At the start of the horizontal part of the combustion stroke
What is the theoretical p-V cycle for a petrol engine called?
Otto cycle
What is the theoretical p-V cycle for a diesel engine called?
Diesel cycle
What assumptions do theoretical cycles for engines make?
1) The same gas is taken continuously around the cycle. This is pure air with adiabatic constant γ = 1.4
2) Pressure and temperature changes can be instantaneous
3) Heat source is external
4) Engine is frictionless
Describe a theoretical p-V diagram for an Otto cycle, starting in the bottom right.
Adiabatic compression: • Curve to the top left Isovolumetric combustion: • Vertical line upwards Adiabatic expansion: • Curve to the bottom right Isovolumetric cooling: • Vertical line downwards
(See diagram pg 234 of revision guide)
Describe a theoretical p-V diagram for a diesel cycle, starting in the bottom right.
Adiabatic compression: • Curve to the top left Isobaric combustion: • Horizontal line to the right Adiabatic expansion: • Curve to the bottom right Isovolumetric cooling: • Vertical line downwards
(See diagram pg 234 of revision guide)
Remember to practise drawing out the actual and theoretical p-V diagrams for a petrol and diesel engine.
Pg 234 of revision guide
How can you tell apart the p-V cycles for a petrol and diesel engine?
- Petrol engine -> Has vertical straight part
* Diesel engine -> Has horizontal straight part
What are the main reasons why engines are less efficient in reality than in theory?
1) Corners of a real engine are rounded, since inlet and exhaust valves take time to open and close
2) In a petrol engine, the heating does not take place at a constant volume, since the pressure and temperature changes would have to be instantaneous
3) There is a small amount of negative work done in real engines between the induction and exhaust lines, since it is not the same air that cycles round the system continuously.
4) Real engines have an internal heat source, not an external one. This means the temperature rise is not as large as in theoretical ones since combustion is incomplete. It also means that peak theoretical pressure is higher than the real one.
5) Adiabatic compression and expansion are not achieved in reality.
6) In reality, energy is needed to overcome friction caused by moving parts of a real engine, so the area inside the loop is smaller for real engines.
Summarise simply the main reasons why engines are less efficient in reality than in theory.
1) Rounded corners
2) Petrol engine -> Isovolumetric heating
3) Work done in induction and exhaust
4) Internal heat source -> Incomplete combustion
5) Not adiabatic compression and expansion
6) Friction
What gives the work done in one cycle of a p-V diagram for an engine?
The area inside the loop.
What is indicated power?
The net work done by an engine in one second.
What is the equation for indicated power of an engine?
Indicated power = Area of p-V loop x No. of cycles per second x Number of cylinders
Where in an engine does friction occur?
Between moving parts
e.g. between the piston and the cylinder
What is friction power?
The power needed to do the work needed to overcome friction in an engine.
What is brake power?
The useful output power of an engine.
What is the equation for friction power?
Friction power = Indicated power - Brake power
What is the proper name for the output power of an engine?
Brake power
What is the equation for brake power?
P = Tω
Where:
• P = Power (W)
• T = Torque (Nm)
• ω = Angular velocity of crankshaft (rad/s)
What is an engine crankshaft?
The part that converts the up/down motion of the piston in the cylinder into rotational motion.
(See diagram pg 235 of revision guide)
What is the input power of an engine?
The amount of heat energy per unit time that an engine could potentially gain from burning fuel.
What is the calorific value of a fuel?
How much energy the fuel has stored per unit volume.
What is the equation for input power?
Input power = Calorific value x Fuel flow rate
What are the different types of engine power and what does each mean?
- Input Power -> The amount of heat energy per unit time that an engine could potentially gain from burning fuel
- Indicated Power ->The net work done by the engine in one second (area of p-V loop)
- Friction Power -> The power needed to do the work needed to overcome friction in an engine.
- Brake Power -> The useful output power of an engine.
Describe how the different types of engine power are linked.
- The input power is the amount of energy that could potential be provided to the engine by fuel.
- Some of this power is converted as indicated power, which is the net work done by the engine’s cylinders.
- The indicated power is split between friction power (used to overcome friction) and brake power (the useful power output).
What are the 3 types of engine efficiency?
- Mechanical efficiency
- Thermal efficiency
- Overall efficiency
What is the mechanical efficiency of an engine?
The proportion of the engine’s output that is converted to useful brake power.
What is the thermal efficiency of an engine?
How well heat energy (from the fuel) is transferred into work.
What is the overall efficiency of an engine?
How effectively the heat from the fuel is transferred into useful output power.
What is the equation for mechanical efficiency?
Mechanical efficiency = Brake power / Indicated power
NOTE: Not given in exam!
What is the equation for thermal efficiency?
Thermal efficiency = Indicated power / Input power
NOTE: Not given in exam!
What is the equation for overall efficiency?
Overall efficiency = Brake power / Input Power
NOTE: Not given in exam!
An engine with an overall efficiency of 36% has an input power of 123kW. The indicator diagram shows the engine has an Indicated power of 53kW. Calculate the mechanical efficiency of the engine.
- Brake power = 0.36 x 123,000 = 44,280 W
* Mechanical efficiency = Brake power / Indicated power = 44,280 / 53,000 = 0.835 = 84% (to 2 s.f.)
What do heat engines convert from and to?
From heat energy into work.
What is the second law of thermodynamics?
- No engine is 100% efficient
* All heat engines must operate between a heat source and a heat sink.
What forms is the heat energy transferred to a heat engine converted to?
- Work done by the engine
* Heat energy transferred to a sink
What happens if the engine temperature is the same as the temperature of a heat sink?
The heat engine cannot operate.
What is a heat sink?
A region that absorbs heat from an engine.
What would be theoretically possible if the second law of thermodynamics didn’t exist?
All of the heat energy supplied to a heat engine could be transferred into useful work.
With heat engines, what is Q(H)?
The heat transferred to OR from a hot region.
With heat engines, what is Q(C)?
The heat transferred to OR from a cold region.
In heat engines, what is W?
The useful work done by the heat engine.
In a heat engine, what is T(H)?
The temperature of the hot region.
In a heat engine, what is T(C)?
The temperature of the cold region.
In a heat engine, what equation relates Q(H), Q(C) and W?
Q(H) = Q(C) + W
Where:
• Q(H) = Energy transferred from the heat source
• Q(C) = Energy transferred to the heat sink
• W = Useful done by the engine
(NOTE: Not given in exam!)
Remember to practise drawing out the flowchart for a heat engine.
See diagram pg 236 of revision guide
Remember to ask the teacher what type of efficiency W/Q(H) is.
Do it. Pg 236 of revision guide.
What is the equation for the efficiency of a heat engine?
Efficiency = W / Q(H) = (Q(H) - Q(C)) / Q(H)
Where:
• W = Useful work output
• Q(H) = Heat transferred from the heat source
• Q(C) = Heat transferred to the heat sink
What is the equation for the maximum theoretical efficiency of a heat engine?
Maximum theoretical efficiency = (T(H) - T(C)) / T(H)
Where:
• T(H) = Temperature of the heat source (K)
• T(C) = Temperature of the heat sink (K)
Why are real heat engine’s efficiencies lower than their theoretical maximum?
1) Frictional forces inside the engine
2) Incomplete combustion of fuel
3) Energy is needed to move internal components of fuel
How is waste heat from a heat engine made useful?
Combined heat and power (CHP) plants reuse the heat for other purposes (e.g. heating nearby houses)
What are reversed heat engines?
Machines that use work to transfer heat from a cold region to a hot region.
Which if these does work and which has work done on it:
• Heat engine
• Reversed heat engine
- Heat engine -> Does work
* Reversed heat engine -> Has work done on it
Remember to practise drawing out the flowchart for a reversed heat engine.
See diagram pg 238 of revision guide
What are the two types of reversed heat engines you need to know about?
- Heat pumps
* Refrigerators
What do a refrigerator and heat pump aim to do?
- Refrigerator -> Extract as much heat energy from the cold space as possible per joule of work done
- Heat pump -> Pump as much heat energy into the hot space per joule of work done
What is a heat pump used for?
Heating rooms and water in homes.
What is COP?
- Coefficient of performance
- A measure of how well the heat is transferred in a reverse heat engine per unit work done
- It can be thought of as the efficiency of a reverse heat engine
What does a COP of 4 mean?
4J of heat energy are transferred per 1J of work done
What are the units for the COP?
No units
What is the equation for the COP of a refrigerator?
COP(ref) = Q(C) / W = Q(C) / (Q(H) - Q(C))
Where:
• COP(ref) = Coefficient of performance of refrigerator
• Q(C) = Heat transferred from the cold space (J)
• Q(H) = Heat transferred to the hot space (J)
• W = Work done (J)
What is the equation for the COP of a refrigerator running at maximum theoretical efficiency?
COP(ref) = T(C) / (T(H) - T(C))
Where:
• COP(ref) = Coefficient of performance of refrigerator
• T(C) = Temperature of the cold space (J)
• T(H) = Temperature of the hot space (J)
(NOTE: Not given in exam!)
What is the equation for the COP of a heat pump?
COP(hp) = Q(H) / W = Q(H) / (Q(H) - Q(C))
Where:
• COP(ref) = Coefficient of performance of heat pump
• Q(C) = Heat transferred from the cold space (J)
• Q(H) = Heat transferred to the hot space (J)
What is the equation for the COP of a heat pump running at maximum theoretical efficiency?
COP(hp) = T(H) / (T(H) - T(C))
Where:
• COP(hp) = Coefficient of performance of refrigerator
• T(C) = Temperature of the cold space (J)
• T(H) = Temperature of the hot space (J)
(NOTE: Not given in exam!)
What is it worth remembering about maximum theoretical efficiency equations?
They are the same as the normal equations, except Q(C) is replaced by T(C) and Q(H) is replaced by T(H).
A house installs a heat pump to keep its rooms at 23°C by pumping heat in from the outside. In theory, how much does the coefficient of performance change is the outside temperature rises from 2°C to 10°C?
At 2°C: • COP = 296 / (296 - 275) = 14.09 At 10°C: • COP = 296 / (296 - 283) = 22.76 So the COP increases by: • 22.76 - 14.09 = 8.7 (to 2 s.f.)
