thermodynamics and engines Flashcards
first law of thermodynamics
describes how energy is conserved in a system through heating, cooling and doing work
equation for first law of thermodynamics
Q = △U + W
U = internal energy
positive and negative Q
+Q = energy transferred to system
-Q = energy transferred away from system
non-flow process
a process which occurs in a closed system
no gas flows in or out the system
condition to apply first law of thermodynamics to a closed system
gas has to be ana ideal gas
means energy is only dependent on the temperature
need to assume that if any work is done there is a change in volume
ideal gas equation
pV = nRT
p1 V1 / T1 = P2 V2 / T2
positive and negative meaning for work done
+W = work done by the system
-W = work done on the gas
isothermal
a process in which the temperature of the system remains constant
as internal energy is dependent on only temperature, △U = 0
so Q = W
what does it mean when Q = W
supplying heat energy to the system will result in an equivalent amount of work being done by the gas (volume increases)
if work is done on system then an equivalent amount of energy is lost
isothermal equations
pV = constant
p1 V1 = p2 V2
adiabatic process
a process in which no heat is gain or lost in a system
Q = 0
so △U = -W
what does △U = -W mean
any change in the internal energy is caused by work done on/by system
if work is done by system then internal energy will decrease by the equivalent amount vice versa
adiabatic process equations
pV^γ = constant
p1 V1^γ = p2 V2^γ
changes at a constant pressure equation
W = p△V
V1 / T1 = V2 / T2
Changes at a constant volume
W = 0 so Q = △U
means all of the heat transferred to/out the system goes directly to increasing/decreasing internal energy
p / T = constant
p1 / T1 = p2 / T2
p/V graph
arrow drawn to indicate in which direction the change is happening
area under = magnitude of work done
isotherm
p ∝ 1/V
isothermal expansion = right
isothermal compression = left
the higher the temperature the further the curve is from the origin
p-V diagrams for adiabatic processes
have a steeper gradient than a isotherm
area is larger than isotherm curve so more work is done to compress a gas adiabatically than isothermally
the gas does less work if it expand adiabatically instead on isothermally
cyclic process
a system can go through different processes to form a loop
net work done of cyclic curve
find the difference between work done by the system and work done to the system
work done per cycle = area of loop
four stroke engines
engines which burn fuel once every four strokes of a piston
internal combustion engines
contains cylinders filled with air
air is mixed with fuel, which is then burned, releasing a large amount of energy
the air fuel mixture is trapped by two tight fitting pistons which move up and down
induction
piston starts at top of cylinder and moves down, increasing the volume of the gas above it
this sucks in a mixture of air and fuel in the open inlet valve
pressure remains constant, just below atmospheric pressure
indictaor diagram is straight horizontal line
compression
inlet valve is closed and the piston moves back up
work is done on the gas increasing the pressure
just before the piston is at the end of the stroke, the spark plug creates a spark which ignites the air-fuel mixture
temperature and pressure increases at an almost constant volume
expansion
hot air-fuel mixture expands and does work on the piston pushing it downwards
work done by gas to expand is more than work done on gas to compress as it has a higher temperature
just before the piston is at the end of the stroke the exhaust valve opens reducing the pressure
exhaust
piston moves up cylinder and the burnt gas leaves through the exhaust valve
pressure remains almost constant, just above atmospheric pressure
four stroke diesel engines
same four strokes but have differences
-in the induction stroke only air is sucked in, not a air-fuel mixture
-dont have spark plug so in compression stroke, air is just compressed until it reaches a temperature high enough to ignite diesel fuel
just before the stroke ends, diesel is sprayed into the cylinder through a fuel injector and ignites
expansion and exhaust stroke is the same
how the four stroke diesel engine induction diagram differs
flatter top showing the point at which diesel fuel is injected and heats up to combustion temperature
theoretical indicator diagrams
petrol engine = otto cycle
diesel engine = diesel cycle
both models make the following assumptions-
-same gas is continuously taken around the cycle. gas is pure air with a adiabatic constant of 1.4
-pressure and temperature chnages can be instantaneous
-heat source is external
-engine is frictionless
theoretical cycle for the four stroke petrol engine
A) gas is compressed adiabatically
B)heat is supplied while volume is kept constant
C)gas is allowed to cool adiabatically
D)system is cooled at a constant volume
theoretical cycle for a four stroke diesel engine
A)gas is adiabatically compressed
B)heat is supplied but pressure is kept constant
C)gas is allowed to cool adiabatically
D) system is cooled at a constant volume
comparing theoretical and real life diagrams
engineers use this to show how well the engines are performing
-corners of theoretical diagram are not rounded as its assumed same air is used continuously
irl corners are rounded as inlet and exhaust valves let in new air and burnt gas out
-irl heating doesn’t take place at a constant volume as an increase in pressure and temperature wouldn’t be instantaneous
-theoretical model doesn’t include the small amount of negative work caused by the loop between induction and exhaust lines as it assumes the same air circulates
-engines have an internal heat source, not an external one, means temperature rise is not as large as the theoretical one as fuel used to to heat the gas is not completely burned in the cylinder
-energy is needed to overcome friction caused by moving parts irl so net work done will always be less than theoretical model
indicated power
net work done by cylinder in one second
can think of indicated power of as maximum theoretical power generated by the gases in the engine cylinders
indicated power equation
indicated power of engine = area of p-V loop x no. cycles per second x no. cylinders
crankshaft
a piston moving up and down in an engine is connected to a crankshaft by a rigid rod
this converts the up and down motion of the piston into a rotational motion
the greater the pressure on the piston (hence the larger the force generating the up and down motion), the greater the rotational motion (torque) generated
output (brake) power
the useful power output at the crankshaft
P = Tw
friction power
friction occurs between many moving parts of an engine, for example between the piston and the cylinder, at the bearings and when the valves are opened and closed
work needs to be done to overcome friction in the engine
the power needed to do this is called friction power. This means that the brake power of the engine is less than the indicated power
friction power = indicated power - brake power
input power
input power is the amount of heat energy per unit time it could potentially gain from burning fuel
input power = calorific value x fuel flow rate
the calorific value
the calorific value of fuel tells you how much energy the fuel has stored in it per unit volume
mechanical efficiency
affected by the amount of energy lost through moving parts (e.g. through friction)
its the ratio of the power generated by cylinders to the power output at the crankshaft
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
second law of thermodynamics
heat engines must operate between a heat source and a heat sink
heat engines
convert heat energy into work
no engine can transfer all heat energy its supplied into useful work though
some heat will always end up increasing the temperature of the engine
if the engine reaches the temperature of the heat source then no work is done
heat sink
a region which absorbs heat from the engine, if not then the engine will reach the temperature of the heat source and no work will be done
heat engines explained
heat energy transferred to engine from heat source = Qh
some of this energy is transferred into useful work but some enrgy must be transferred into the heat sink, Qc which has a lower temperature
means heat engines cant be 100% effecient
heat engine efficiency
W / Qh = Qh - Qc / Qh
maximum theoretical efficiency
by assuming the perfect conditions
max theoretical efficiency = TH -TC / TH
in practise real heat engines efficiency is lower than its theoretical maximum as energy is lost due to friction and the energy needed to move them
also fuel doesnt burn entirely
so the value of QH is lower in practice
maximising heat engines efficiency
to maximise efficiency as much of the input heat must be transferred usefully
however heat engines are very inefficient as there is a lot f waste heat which is transferred to surroundings and lost
combined heat and power plants
CHPs try to limit energy waste by using waste heat for other uses like heating nearby houses and buildings
reversed heat engines
operate between hot and cold reserviours like other engines
heat is taken from the cold space and put in the hot space
heat natuurally flows from hot to cold so work has to be done to do this
input/output of work for heat engines
heat engine = output of work
reverse heat engine = input of work
refridgerators
aims to extract as much heat as possible from cold sace and exert into the suroundings for each joule of work done
work is done to transfer heat away from cold space via pipes on the back of the appliance
heat pumps
cold space is outside hot space inside
aims to pump as much heat as possible to hot space per joule of work done
used to heat rooms and water inside homes
coefficient of performance
reverse heat engines are judged on how well they can transfer heat based on the amount of work done on them
a measure of how well this work is converted into heat transfer
COP example
COP of 4 transfers 4J of heat energy for every 1J of work done
a COP greater than 1 means the amount of energy transferred is more than the work done needed to transfer it
the higher the COP the lower the running costs
COP for refridgerators
as its heat is removed from cold space important
COP = QC / W = QC / QH - QC
maximum theoretical effieciency COP
COP = TC / TH - TC
COP for heat pumps
as heat is transferred to hot space thats important
COP = QH / W = QH / QH - QC
max theoretical effeciency COP
COP = TH / TH - TC
