Unit 5: Thermodynamics and engines Flashcards
What is thermodynamics?
The study of the relationship between heat and other forms of energy
What do equations of state involve i.e. the three gas laws?
Pressure, volume and temperature
What is Boyle’s law in words?
For a fixed mass of gas at a constant temperature, the product of the pressure and volume is constant
What is the equation for Boyle’s law?
pV = constant or p is proportional to 1/V at constant T
What is Charles’ law in words?
For a fixed mass of gas at constant pressure, the volume is directly proportional to the temperature measured in kelvin
What do gas laws apply only to?
A fixed amount of gas
What is the equation for Charles’ law?
V/T = constant or V is proportional to T at constant p
What is the definition of 1 kelvin?
A temperature change of 1 kelvin is identical to a temperature change of 1°C, the kelvin and celsius scales have equal increments but they start at different places: 0K = -273.15°C
What is the pressure-temperature law in words?
For a fixed mass of gas at constant volume, the pressure is directly proportional to the temperature measured in kelvin
What is the equation for the pressure-temperature law?
p/T = constant or p is proportional to T at constant V
Do real gases obey the gas laws exactly?
No
What do the gas laws give an accurate description of?
The way gases behave at low temperatures and temperatures that are well above their liquefaction temperature
What is the equation for the ideal gas law and what do the terms in it represent?
pV = nRT where V is the volume in m^3, T is the temperature in kelvin, p is gas pressure in Nm^-2 or Pa, R is the universal molar gas constant = 8.31 JK^(-1)mol^(-1) and n is the number of moles
What can be said about a gas that obeys the ideal gas law exactly?
This gas has exactly no forces acting between the molecules and hence the internal energy (energy of molecules) is entirely kinetic and depends only on its temperature
What does the first law of thermodynamics relate?
Heat and work and it is essentially the principle of the conservation of energy
What is the equation for the first law of thermodynamics and what do the terms represent?
Q = ΔU + W where Q is the heat entering the system, ΔU is the increase in internal energy and W is the work done by the system
How can internal energy be increased?
By doing work on the system i.e. compressing it or putting energy into the system
What does the change in internal energy depend on?
The change depends on the initial and final states of the system and not how the change was brought about
What is an isolated system?
A system cut off from any external influence
What are the conditions of an isolated system?
No work can be done hence W = 0, no heat can enter or leave the system hence Q = 0 therefore ΔU = 0 and the internal energy of an isolated system is constant
When do adiabatic process occur?
They occur very rapidly or in a system that is so well insulated that no transfer of energy as heat can occur between the system and its external environment
What is the condition for a adiabatic process?
Q = 0
What does the first law of thermodynamics change to in an adiabatic process?
ΔU = -W
What is the definition of internal energy?
The internal energy of a system is the sum of the kinetic and potential energies of the atoms and molecules comprising the system, the value of the absolute internal energy of a system cannot be measured, only its change from one state into another
What is an isothermal process?
A process that takes place under constant temperature conditions
What is the formula for an isothermal process in terms of pressure and volume?
pV = constant
What is the formula for an isothermal process in terms of the first law of thermodynamics?
Q = W as ΔU = 0
What is necessary if a gas is to maintain its temperature when it expands?
If a gas expands and does external work W, an amount of heat Q has to be supplied to the gas in order to maintain its temperature and vice versa
What is required to produce an isothermal change ?
It requires a gas to be kept in a thin-walled vessel that is composed of an excellent conducting material surrounded by a constant temperature bath - any expansion or contraction within the system must take place slowly, under such conditions the process can be reversed and returned to its initial state i.e. the process is reversible
In practice, is it possible to produce a perfectly reversible change?
No
What is the formula for a reversible isothermal change?
p1V1 = p2V2
What is an adiabatic process?
A process that takes place in such a way that no heat can enter or leave the system
What is the formula for an adiabatic process in terms of pressure and volume and when can this formula be applied?
pV^Ɣ = constant and this formula can be applied when a gas undergoes a reversible adiabatic expansion or contraction
What does Ɣ depend on?
The molecular structure of the gas
What is the formula for Ɣ?
Ɣ = cp/cv
What is the formula for an adiabatic process in terms of the first law of thermodynamics?
W = -ΔU as Q = 0
In an adiabatic process, what happens when a gas expands and does external work?
Its temperature falls and vice versa
Is a truly adiabatic process possible?
No
What processes can produce near-adiabatic conditions?
Processes that can happen suddenly and rapidly such as the rapid expansion and contraction of air when sound waves pass through
What is the formula for an adiabatic process when there are two gases involved for instance?
p1V1^Ɣ = p2V2^Ɣ OR p1V1/T1 = p2V2/T2 OR T1V1^(Ɣ -1) = T2V2^(Ɣ -1)
What are the conditions for constant-volume processes?
The system can do no work if the volume of a system such as a gas is held constant, if heat is absorbed by the system (Q is positive) then the internal energy of the system must increase and vice versa
What is the formula for a constant-volume process in terms of the first law of thermodynamics?
ΔU = Q as W = 0
What is the formula for a constant-volume process in terms of cv?
Q = cvΔT
What is cv?
Cv is the molar heat capacity of a gas at constant volume, it is the heat required to produce unit temperature rise in one mole of the gas when the volume remains constant
What is the external work done by an expansion of a gas at constant pressure?
W = pAΔs where A is the cross-sectional area and Δs is the small distance moved by the piston
What is work done equal to in terms of pressure and volume?
W = pΔV
What is the formula for a constant-pressure process in terms of cp?
Q = cpΔT
What is cp?
Cp is the molar heat capacity of a gas at constant pressure, it is the heat required to produce unit temperature rise in one mole of the gas when the pressure remains constant
What is a restriction and consequence of an isothermal process?
The restriction is that ΔU = 0 and the consequence is that Q = W
What is a restriction and consequence of an adiabatic process?
The restriction is that Q = 0 and the consequence is that W = -ΔU
What is a restriction and consequence of a constant volume process?
The restriction is that W = 0 and the consequence is that ΔU = Q
What is a restriction and consequence of a constant pressure process?
The restriction is that W = pΔV and the consequence is that Q = ΔU + pdV
What is a p-V diagram and what can it also be referred to as?
It is a plot of pressure versus the volume of a gas and it is also known as an indicator diagram
What is the formula for work done in terms of pressure?
It is the integral of p with respect to volume between the initial and final volume
What is represented by the area under a p-V diagram?
The work done
What does the area of a loop represent?
The work done per cycle
Does a gas do work in a compression?
Work is done on the gas in a compression
What is an engine?
A device or system that extracts energy from its environment in the form of heat and converts it into useful work
What is present in every heat engine?
A working substance
What does an internal combustion engine use?
A petrol-air mixture
What does a steam engine use?
Water
What is necessary for an engine to be useful?
They must work continuously and work in a cycle i.e. the working substance must pass through a series of thermodynamic processes
What is the idealised four-stroke petrol engine cycle also referred to as?
The Otto cycle
In a p-V diagram for a real engine, are the corners sharp or rounded?
Rounded
What is the order of the strokes in an idealised four-stoke petrol and diesel engine cycle?
Induction stroke, compression stroke, power stroke, exhaust stroke.
What happens in the induction stroke of an idealised four-stroke petrol engine cycle?
The inlet valve opens and the exhaust valve closes, the piston moves down. During this time, a mixture of typically 7% petrol vapour and 93% air at about 50°C is drawn into each cylinder.
What happens in between the induction stroke and compression stoke in an idealised four-stroke petrol engine cycle?
The inlet valve closes
What happens in the compression stroke of an idealised four-stroke petrol engine cycle?
The piston moves up, compressing the gas adiabatically. The temperature rises to 300°C.
What happens in between the compression stoke and the power stroke in an idealised four-stroke petrol engine cycle?
A spark plug ignites the gas mixture supplying heat (Qin) and increasing the pressure at constant volume. The temperature rises to 2000°C.
What happens in the power stroke of an idealised four-stroke petrol engine cycle?
The increased pressure pushes the piston down as the gas expands adiabatically, decreasing both the pressure and the temperature
What happens in between the power stroke and the exhaust stroke of an idealised four-stroke petrol engine cycle?
The exhaust valve opens and most of the burnt gas mixture is released, removing an amount of heat (Qout). The pressure and temperature of the gas that remains in the cylinder decrease rapidly
What happens in the exhaust stroke of an idealised four-stroke petrol engine cycle?
As the piston moves up, the remaining gas mixture is expelled.
What happens after the exhaust stoke of an idealised four-stroke petrol engine cycle?
The exhaust valve closes and the inlet valve opens. The cycle repeats.
Is the efficiency of an actual engine less than that predicted on theoretical grounds?
Yes
Why is the efficiency of a real petrol engine less than that theoretically predicted?
The petrol-air mixture does not behave as an ideal gas, and the efficiency is further reduced by frictional effects, turbulence, loss of heat to the cylinder walls and the fact that the inlet and exhaust valves take a finite time to open and close
What is efficiency a measure of?
The performance of an engine
What is thermal efficiency in words?
The ratio of the work done by the engine to the heat supplied
What happens before the induction stroke of an idealised diesel engine cycle?
The inlet valve opens and the exhaust valve closes
What happens in the induction stroke of an idealised diesel engine cycle?
Air is drawn into each of the cylinders at atmospheric pressure as the piston moves down
What happens in between the induction stroke and the compression stroke of an idealised diesel engine cycle?
The inlet valve closes
What happens in the compression stroke of an idealised diesel engine cycle?
The air in the cylinder is compressed adiabatically as the piston moves up. The temperature of the air rises to 700°C and becomes hot enough to ignite the fuel.
What happens in the first part of the power stroke for the idealised diesel engine cycle?
Diesel fuel is sprayed into the cylinder and is ignited immediately by the hot air, suppling heat (Qin). This forces the piston to move down at constant pressure and is the first part of the power stroke
What happens in the second part of the power stroke for the idealised diesel engine cycle?
The fuel supply is cut off and the burnt gas expands adiabatically. This forces the piston down and the temperature falls.
What happens in between the power stroke and the exhaust stroke of an idealised diesel engine cycle?
The exhaust valve opens and releases the exhaust gas, removing an amount of heat (Qout). The pressure and temperature of the gas remaining in the cylinder decrease accordingly
What happens in the exhaust stroke of an idealised diesel engine cycle?
The remainder of the gas is expelled from the cylinder as the piston moves up
What happens after the exhaust stroke of an idealised diesel engine cycle?
The exhaust valve closes, the inlet valve opens and the cycle is repeated
What is a similarity between petrol and diesel engines?
They both have four-stroke cycles
Why are diesel engines much more efficient than petrol engines?
For a diesel engine, there is no fuel in the cylinder during compression therefore much higher compression ratios can be achieved (16:1 for diesel and 10:1 for petrol)
Why are diesel engines more expensive to produce?
Diesel engines operate at higher working pressures than petrol engines
What type of engine has a lower power-to-weight ratio?
Diesel engines
What is the compression ratio?
The ratio of the volume enclosed in the cylinder at the beginning of the compression stroke to the volume enclosed at the end of the stroke
In real engines, why are there no sharp changes?
The valves need time to open and close
What can be said about the compression and expansion strokes in a real engine?
They are not truly adiabatic because heat losses occur
What can be said about maximum temperature in a real engine?
The maximum temperature is not attained because of imperfect combustion
What can be said about heating in a real engine?
Heating is not achieved at constant volume because the pistons are always moving
How can the measurement of the power of an engine be determined or estimated at several points?
In the transmission of the power from its generation to its application
What is the formula for input power?
Pinput = calorific value of fuel (Jkg^(-1)) x fuel flow rate (kgs^-1)
What is the fuel flow rate dependent on?
The state of the motion of the car, how it is driven, the type of engine and the state of the tyres
What is the indicated power of an engine in words?
The theoretical capability of the power of an engine
What is the formula for the indicated power of an engine?
Pind = area of p-V loop (J) x number of cycles per second (s^-1) x number of cylinders
Why is the indicated power the maximum theoretical power output of an engine?
It assumes frictionless motion
How often does a power cycle occur and why?
It occurs once every two revolutions to allow the engine to go through all four of its strokes
What is the usual method of determining the work done?
By counting the squares under a graph and calculating what the area of one square represents i.e. the scaling factor
What is the output/brake power of an engine?
A measure of the engine’s power without the loss in power caused by the gearbox, alternator, differential, water pump and other auxiliary components
What is the output power in terms of the crankshaft and what is it more usually referred to as?
It is the power delivered to the engine’s crankshaft (i.e. the engine’s flywheel) and is more usually referred to as brake horsepower (bhp)
What is the definition of horsepower?
The horsepower is not an SI unit, although it is still in common use: 1 horsepower = 746W.
What is the output/brake power proportional to?
The product of the output torque and the number of revolutions per minute
What is the formula for output/brake power?
Pout = Tω
What is the formula for frictional power?
Pfriction = indicated power - output/brake power = Pind - Pout
What is the formula for the mechanical efficiency of an engine?
η = output power/indicated power = Pout/Pind
What is the formula for the thermal efficiency of an engine?
ε = indicated power/input power = Pind/Pinput
What is the formula for overall efficiency?
η x ε = output power/input power = Pout/Pinput
What is the purpose of any engine?
To transform as much as possible of the extracted energy Qin into work
What is the condition for an idealised heat engine?
ΔU = 0
Within the heat engine, is there any loss of energy?
No
What is the formula for the work done by a heat engine?
W = Qin - Qout
What does thermal efficiency measure?
The success of the heat engine
What is thermal efficiency defined as?
The work the engine does per cycle (the energy we get) divided by the energy it absorbs as heat per cycle (the energy we pay for)
What is the formula for thermal efficiency in terms of work done?
work done in one cycle/heat taken in at the higher temperature = W/Qin = Qin-Qout/Qin = 1 - (Qout/Qin)
What is the formula for the maximum theoretical efficiency?
εmax = Th - Tc/Th = 1 - Tc/Th
What does Th represent in the maximum theoretical efficiency formula?
The temperature of the hot reservoir (source) in kelvin
What does Tc represent in the maximum theoretical efficiency formula?
The temperature of the cold reservoir (sink) in kelvin
When does the formula for the maximum theoretical efficiency apply?
It is valid for all reversible engines, irrespective of the particular cycle and the particular working substance
Why is there no change in the internal engine of an idealised heat engine?
At the completion of the cycle, the engine’s working substance is in the same state as it was initially
Why does a heat engine have a theoretical efficiency less than 1?
Th > Tc
What should ideally happen in a heat engine?
The heat should be taken entirely at the single temperature Th and rejected at the single temperature Tc
Why are the efficiencies considerably less than that indicated in a real engine?
The heat is usually taken in over a range of temperatures and rejected over a range of temperatures, there are additional losses due to frictional effects, turbulence and other factors
How do designers try to improve engine efficiency?
Reducing the energy Qout that is thrown away during each cycle
What would need to happen to achieve the perfect engine?
Tc = 0 (absolute zero) and Th to approach infinity and both requirements are impossible to attain
How can the efficiency of a heat engine be increased?
By taking in heat at as high a temperature as possible and rejecting heat at as low a temperature as possible
Does any heat engine convert heat completely into work?
No
What occurs when a cold body and a hot body are brought into contact?
Heat always flows from the hot body to the cold body
What does the second law of thermodynamics state?
It is not possible to convert heat continuously into work without at the same time transferring some heat from a warmer body to a colder body
What does the second law of thermodynamics show?
The conditions under which heat can be converted into work and in particular, it states that heat cannot be converted completely into work
What can be said about the processes of a real engine?
The processes that form the engine cycle are not reversible
What is the formula for power in terms of work done?
P = W/t
What are refrigerators?
Heat engines that work in reverse i.e. that take heat in at low temperatures and reject heat at higher temperatures
How do refrigerators work?
They use work to transfer energy from a low-temperature reservoir to a high-temperature reservoir as it continuously repeats a set of thermodynamic processes
In practice what is required to make a refrigerator work?
Some external device e.g. an electric motor or compressor has to do work on the working substance of the system to transfer energy from say a food storage compartment (low-temperature reservoir) to a room (high-temperature reservoir)
What are two types of refrigerators?
Heat pumps and air conditioners
For a heat pump that is used to heat a house, what are the high-temperature and low-temperature reservoirs?
The room to be heated is the high-temperature reservoir and heat is transferred to it from the cooler outdoors
For an air conditioner, what are the high-temperature and low-temperature reservoirs?
The low-temperature reservoir is the room to be cooled and the high-temperature reservoir is the warmer outdoors
What is the purpose of a heat pump?
To supply heat to the high-temperature reservoir
What is the purpose of the refrigerator?
To remove heat from the cold reservoir
What determines the effectiveness of both heat pumps and refrigerators?
The coefficient of performance
What is the COP in words?
The ratio of the heat extracted or supplied to the work done by the external agency
What is the formula for the COP of a refrigerator?
COPref = Qout/W = Qout/Qin - Qout
What is the formula for the maximum COP of a refrigerator?
COPmax = Tc/(Th - Tc)
What is the formula for the COP of a heat pump?
COPhp = Qin/W = Qin/(Qin-Qout)
What is the formula for the maximum COP of a heat pump?
COPmax = Th/Th-Tc
Why do heat pumps provide an extremely low-cost and efficient form of heating?
The heat supplied Qin is much greater than the work done by the external device i.e. Qin - Qout
How can a higher COP value be obtained?
The value of the COP is higher the closer the temperatures of the two reservoirs are to each other i.e. when Th is approximately equal to Tc
When do heat pumps work more effectively?
In temperate climates than in climate where the temperatures vary considerably
