Thermodynamics Flashcards
Engineering materials
intensive properties and extensive properties
are defined as substances which are manufactured and used for various
engineering applications.
these are properties independent to mass of system Ex temp, pressure
(its same at all points of the system)
these are properties dependent on mass
ex. volume, mass
(its the sum of all the values of the property at different point)
what is isothermal, isobaric,
isochoric,
isentropic
temp remains constant
pressure remains constant
Volume remains constant
entropy remains constant
Quasi-static or Quasi
and what is a process
Equilibrium process during which the course of deviation from thermodynamic equilibrium is negligibly small
when a system undergoes a change of state, it is said to have undergone a process, the values of properties change
what is temperature
equality of temperature
what is thermodynamic equilibrium
its the measure of hotness or coldness
two systems or a system and its surroundings are said to have equality if there is no change in observable property when they are bought in thermal contact
when no change in macroscopic property is observed after it is isolated from its surroundings
Zeroth law of thermodynamics
First law of thermodynamics for cyclic process
when system A and B are independently in thermal equilibrium with a third system say C, then they are in thermal equilibrium with each other
when a system undergoes a cyclic process, the algebraic sum or cyclic integral, of heat transfers is proportional to, the algebraic sum (or cyclic integral), of work transfers
The first law of thermodynamics states that energy can neither be created nor destroyed, only altered in form
(conservation of energy)
what are the three types of temperature measurement
what is reference system and property
what is thermometric property
Reference System and property, Reference points
Formation of Temperature Scales
REFERENCE SYSTEM
referred to as the thermometer and possesses a property that is measurable and changes with temp
THERMOMETRIC PROPERTY
the property that changes with temp increase
what are Reference points
why was two fixed points abandoned
they are distinct points and reproducible states at any places on the earth
ex ice melting
steam point etc
2 POINTS ABANDONED:
extreme sensitiveness to change in pressure for steam point
difficulty of achieving equilibrium between pure ice and air saturated water, as ice melts
when is work positive and negative
and
when is heat in a system positive and negative
when work is done by the system (+)
when work is done on the system (-)
heat added to a system (+)
heat removed from the system (-)
what is transient phenomena,
Boundary phenomena,
which are path functions
does system possess heat or work or only possesses energy
heat and work are observed only there is transfer of energy and hence are transient in nature
heat and work are observed at the system boundary, change of boundary and the form of energy transfers may change from heat or work vice versa
both heat and work are path functions and hence are inexact differentials
it only possesses energy
what two things are not addressed by the first law
what do you mean heat is qualitatively lower than work done
process follow a definite direction
heat and work are qualitatively different
all work can be dissipated as heat while heat cannot be converted into work done by any device in a working thermodynamic cycle
heat reservoir
,heat source, heat sink
a body of infinite heat capacity, whose temp is not affected by any heat transfer. a body of infinite heat capacity, which can absorb or supply heat without any change in its temperature.
HEAT RESERVOIR and HEAT SINK
is a heat reservoir which can supply heat without any change in its temperature.
is a heat reservoir which can absorb heat without any change in temperature.
what is heat engine
what is reversed heat engine
is a device that works in a thermodynamic cycle and produces net positive work while absorbing heat from a source and dissipating heat to a sink.
formula W=Qh-Ql
REVERSED HEAT ENGINE
is a device that operates in a thermodynamic cycle and transfers heat from a low temperature body (sink) to a high temperature body (source) with the aid of external work.
W=Qh-Ql
Clausius Statement
It is impossible to construct a device that operates in a thermodynamic cycle and transfers heat from a cold body to a hot body without the input of external energy.
principles of refrigeration
The process of cooling or reducing the temperature of a substance below that of the
surrounding atmosphere and maintaining this lower temperature within the boundary of a
given space is called refrigeration.
In order to keep the substance cold, heat must be continuously removed from the given
substance.
According to the law of thermodynamics, heat naturally flows from a hot substance to a cold
substance. But if heat has to flow from a cold substance to a hot substance, some form of work
has to be performed
Refrigeration works on the principle that heat is continuously extracted from the
low temperature substance by performing mechanical work. This heat is then
rejected to the surrounding atmosphere (high temperature level)
mechanical energy definition and shaft, motor formula
The mechanical energy is defined as the form of energy that can be converted
to mechanical work completely and directly by an ideal mechanical device such
as an ideal turbine.
npump=mech power increase/mech power OUT
nturbine=mech power OUT/mech power decrease
Nmotor:mech OUT /electric IN
NGenerator: electric power OUT/mechanical power IN
Nturbine=Pshaft/Phydralic(mgh of water flow)
Pshaft=Pelectric/Ngenerator
Npump-motor:
NpumpNmotor/Nmotor
Nturbine-gen:
NturbineNgen/Ngen
what is an engine
two types of engines
classifications of engines (7)
IC engines can be classified into 3 types:
An engine is a device which transforms one form of energy into another form.
external(combustion takes place outside the engine.)
internal( combustion takes place within the engine.)
CLASSIFICATION
Number of strokes per cycle
Nature of thermodynamic cycle
Ignition systems
Fuel used
Arrangement of
cylinders
Cooling systems
Fuel supply systems
Otto cycle, Diesel cycle, and Dual cycle engines.
HEAT ENGINE
Heat engine is a device which transforms the chemical energy of a fuel
into thermal energy and utilizes this thermal energy to perform useful work. Thus, thermal
energy is converted to mechanical energy in a heat engine
ignition type and its properties
fuel supply system types:
spark ignition :
sparking starts at the end of compression stroke from spark plug
compression ignition:
the temperature of the fuel is increased to the self-ignition point by
compressing the air alone and at the end of compression, fuel is injected into the cylinder.
FUEL SUPPLY
Carburetor engine (mix of air and fuel injection)
Air injection engine, and
Airless or solid or Mechanical injection engines. (use a mechanical pump to deliver fuel into the combustion chamber of an engine.)
define cylinder and piston
It is a hollow cylindrical structure closed at one end
with the cylinder head
The combustion of the fuel takes place inside the
cylinder.
PISTOM
It is a cylindrical component fitted perfectly inside the
cylinder providing vacuum seal
what is a piston, and how is the piston connected to the connecting rod, and name all the pistion rings
what is connecting rod
It is a cylindrical component fitted perfectly inside the
cylinder providing vacuum seal and
connected by the:
the gudgeon pin
ALL rings
compression ring
(upper ring), (compress the air or airfuel mixture )
oil rings (lower rings)
( collect the surplus
lubricating oil on the liner surface.)
to transfer the reciprocating
motion of the piston into rotary motion of the crankshaft.
It connects the piston and the crankshaft
what is crankshaft
in four strokes how many times does the crankshaft rotate
Crankcase
It is principal rotating part of the engine which controls the
sequence of reciprocating motion of the pistons.
four strokes
of the piston or two revolutions of the crankshaft.
CRANKCASE
The bottom portion of the cylinder block is called crankcase. A cover
called crankcase which becomes a sump for lubricating oil is fastened
to the bottom of the cylinder block.
Flywheel
heavy wheel mounted on the crankshaft to minimize the cyclic
variations in speed. It absorbs the energy during the power stroke and
releases it during the non-power stroke.
Displacement or Swept Volume (Vs) meaning and formula
Compression Ratio (r)
Clearance Volume (Vc):
The nominal volume swept
by the working piston when travelling from one dead centre to the
other is called the (cc).
Vs = A*L = pi/4 d^2L
COMPRESSION RATIO
:It is the ratio of the total cylinder volume
when the piston is at the bottom dead centre, Vt , to the clearance
volume, Vc.
Vt/Vc = Vc+Vs/Vc = 1 + Vs/Vc
The nominal volume of the combustion
chamber above the piston when it is at the top dead centre is the
clearance volume
PETROL CYCLE
SUCTION
starts when the piston is at the TDC
and about to move downwards. 0→1
The inlet valve is open exhaust valve is
closed
suction created by the motion of the piston towards the
BDC, the charge of fuel-air mixture is
drawn into the cylinder.
BDC the suction stroke
ends and the inlet valve closes instantaneously.
COMPRESSION
The charge taken into the cylinder during the suction stroke is
compressed by the return stroke of the piston 1→2.
both inlet and exhaust valves are closed
The mixture is now compressed the clearance volume.
end of the compression stroke the mixture is ignited with the
spark plug on the cylinder head.
EXPANSION/ POWER STROKE
high pressure of the burnt gases forces the piston towards the
BDC, (stroke 3→4).
Both the valves are in closed position.
power is produced. Both pressure and temperature decrease during expansion.
EXHAUST STROKE
At the end of the expansion stroke the exhaust valve opens instantaneously and the inlet valve remains closed.
The pressure falls to atmospheric level a part of the burnt gases
escape.
The piston starts moving from the bottom dead centre to top dead
centre (stroke 5→0) and sweeps the burnt gases out from the
cylinder almost at atmospheric pressure.
The exhaust valve closes when the piston reaches TDC.
EXHAUST STROKE
end of the expansion stroke ,exhaust valve opens and the inlet valve remains closed.
The pressure falls to atmospheric level a part of the burnt gases
escape.
The piston starts moving from the BDC to TDC (stroke 5→0) and sweeps the burnt gases out from the cylinder almost at atmospheric pressure.
The exhaust valve closes when the piston reaches TDC.
Diesel Engine cycle
COMPRESSION
during suction stroke, air, instead of a fuel-air mixture
higher compression ratios employed, the temp at the end of the compression
stroke is sufficiently high to self ignite the fuel which is injected
into the combustion chamber.
In CI engines, a high pressure fuel pump and an injector are provided to inject the fuel into the combustion chamber.
SUCTION STROKE
Air alone is inducted
Air is compressed into the clearance volume. Both valves remain closed
EXPANSION
Fuel injection starts nearly at the end of the compression stroke.
The rate of injection is such that combustion maintains the pressure constant in spite of
the piston movement on its expansion stroke increasing the volume
Heat is assumed to have been added at constant pressure.
After the injection of fuel is completed (i.e. after cut-off) the products of combustion
expand. Both the valves remain closed during the expansion stroke.
EXHAUST
The piston travelling from BDC to TDC pushes out the products of combustion.
The exhaust valve is open and the intake valve is closed during this stroke
what is indicated power and brake power
how is brake power identified and formula
torque formula
IP:
The power developed inside the cylinder of the engine
BP:
It is the net power available at the crank shaft of the engine for performing
useful work (BP).
It is always less than indicated power since a part of the power developed in the engine
cylinder is used to overcome the frictional losses at different moving parts of the engine.
The arrangement is known as
dynamometer. Usually, rope brake dynamometer
a device designed to assess the power of an engine shaft by introducing frictional resistance to the shaft’s motion through the use of a rope
2𝜋𝑁𝑇/60×1000 (kW) N=Crank Speed,
TORQUE
= 𝑇 = (𝑊 − 𝑆) ×(𝐷𝑏+𝑑𝑟)/2
W= weight, S=spring balance
Db=diameter of brake drum,
dr=diameter of rope
formula
frictional power
Mechanical efficiency
indicated thermal efficiency and brake thermal efficiency
two specific fuel consumption defintion ways (ISFC), (BSFC)
FP = IP – BP
mech = BP/IP
Nith = 𝐼𝑃/(𝐶𝑉 × 𝑚f)
Nbp = 𝐵𝑃/(𝐶𝑉 × 𝑚𝑓)× 100
CV is the calorific value of the fuel in KJ/kg
mf is mass flow rate of the fuel in kg/s.
units are in kW
Specific fuel consumption
ISFC =𝑴𝒂𝒔𝒔 𝒐𝒇 𝒇𝒖𝒆𝒍 𝒄𝒐𝒏𝒔𝒖𝒎𝒆𝒅 𝒊𝒏 (𝒌𝒈/𝒉𝒓)/𝑰𝒏𝒅𝒊𝒄𝒂𝒕𝒆𝒅 𝑷𝒐𝒘𝒆𝒓 𝒊𝒏 𝒌𝑾
BSFC =
𝑴𝒂𝒔𝒔 𝒐𝒇 𝒇𝒖𝒆𝒍 𝒄𝒐𝒏𝒔𝒖𝒎𝒆𝒅 𝒊𝒏 (𝒌𝒈/𝒉𝒓)
/𝑩𝒓𝒂𝒌𝒆 𝑷𝒐𝒘𝒆𝒓 𝒊𝒏 𝒌W
both mf should be divided by 3600 as it should be per second
Specific fuel consumption – It is the mass of fuel consumed per kW of power developed per hour
and is a criterion of economical power production
Mf=
fuel flow(L)1000specific gravity
fuel flow in default will be in m^3
and should be per/sec
Kg/s => L/s
divide mf/specific gravity
litres should be converted m^3 divided 1000
comparsion of diesel and petrol engine
evaluating the performance of an engine
three factors , and 3 ways to determine them
petrol are lighter engines than diesel,
and the are higher speed(rpms) than diesel,
diesel has higher compression ratios thus
greater thermal efficiency
PERFORMANCE OF ENGINE
diesel engines are heavier due to higher peak pressures compared to petrol engines
Maximum power or torque
Specific fuel consumption
Reliability and durability
By using experimental results obtained from engine tests.
By analytical calculation based on theoretical data
By doing numerical caluculation using theoretical data
MOTOR
battery and list the three types of them
what is a controller in ev
DC/DC converter auxiliary battery
Energy Management System
MOTOR
high torque electric
motor.
While braking, it acts like a generator (regenerative braking) and
recharges the batteries.
BATTERY TYPES
Those are lead acid batteries, nickel metal hydride
(NiMH) batteries and lithium ion (Li – ion) batteries.
CONTROLLER
a computerized motor controller. regulates the
flow of energy from the power pack to the motor in relation to the pressure applied on the accelerator
DC/DC CONVERTER
A 12V auxiliary battery in an electric car to
power all 12V accessories such as lights, horn etc. by cutting battery pack voltage down to 12V
EMS
The brain of EVs that monitors and controls all required functions.
It is a computer based system that optimizes charging and energy
output of batteries to maximize operating range and improve
performance.
Hybrid Electric Vehicle (HEV)
i) Series Architecture
In case of series hybrid system, the mechanical output(IC engine) is first
converted into electricity using a generator.
The converted electricity either charges the battery or can bypass
the battery to propel the wheels via the motor and mechanical
transmission.
Hybrid Electric Vehicle (HEV)
i) Parallel Architecture
The parallel HEV allows both IC engine and electric motor to deliver power to drive the wheels since both IC engine and electic motor aee connected to the shaft via two clutches, the propulsion power may be delivered by IC engine alone, by electric motor alons, or both IC engine and electric motor. The electric motor can be used as a generator by absorbing the battery by regenerative braking or by absorbing power from the IC engine when its output is greater than required for the output for the wheels
Hybrid Electric Vehicle (HEV) – Architectures
iii) Series - Parallel Architecture
what is the advantage of Series - Parallel Architecture
In the series-parallel hybrid, the configuration incorporates the
features of both the series and parallel HEVs.
However, this configuration needs an additional electric machine and
a planetary gear unit making the control complex.
ADV:This setup takes advantage of the strengths of both configurations to maximize efficiency, flexibility, and performance under different driving conditions.
City driving (low speeds): At low speeds or in stop-and-go traffic, a series hybrid mode is more efficient.
At higher speeds, the parallel hybrid mode is more efficient.
HYBRID ELECTRIC VEHICLES (HEV)
difference between series and parallel hybrid
They have two complementary
drive systems: an IC engine with a fuel tank and an electric motor
with a battery.
HEVs cannot be recharged from the electricity grid – all their
energy comes from fuel and from regenerative braking.
difference between series and parallel hybrid:
parallel mode is used when both the electric motor and internal combustion engine (ICE) can provide power simultaneously, while series mode is used when the electric motor is the only source of mechanical power
metal alloys, Steel as an example and alloy steel
ferrous and nonferrous
Ferrous alloys, those in which iron is the principal constituent, include steels and cast irons ex:
STEEL
iron-carbon(less than 2 percent)
The nonferrous ones—all alloys that are not iron based.
alloy steel
Steels which acquire some characteristic properties due to the addition of
alloying elements other than Carbon; for specific properties
low, medium, high carbon steels
0.25% Carbon
Relatively soft and weak
Outstanding Ductility and Toughness
Very good Machinability and Weldability
eg. Mild Steel
Least expensive to produce
Unresponsive to hardening heat treatment
Very low hardenability
Automobile body components
Structural shapes (I beams, Angle Irons); Sheets used in tin
cans, buildings etc.
medium carbon steel
0.25% to 0.6 carbon
Stronger than Low Carbon Steels
Less tougher
Best range for adding alloying elements
Good mix of ductility and strength
Railway wheels and tracks Gears
Crankshafts and other machine parts
High carbon steels
From 0.6% to 1.4% carbon
Hardest Strongest
Least ductile when compared with Low Carbon and Medium
Carbon Steel
Best range to make tool steels
Cannot be used for operations where ductility and
malleability are required
Knives ; Razors ; Hacksaw blades ; High strength Wires
CAST IRONS, CAST IRONS types
distinct limitations, chiefly
alloys having carbon content above 2.1% by weight, most cast irons contain carbon between 3 – 4.5% by weight and in addition
Cast Irons are also very brittle. Therefore, casting is the most convenient fabrication
technique.
1) Gray Cast Iron
2) Nodular or Ductile Cast Iron
3) White Cast Iron
4) Malleable Cast Iron
DIS ADVANTAGES
a relatively high density,
a comparatively low electrical conductivity, and
an inherent susceptibility to corrosion in some common environments.
GRAY CAST IRON
DUCTILE OR NODULAR CAST IRON
white cast iron
MALLEABLE CAST IRON
2.5% to 4% Carbon
1% to 3% Silicon
Weak and brittle in tension
Higher Compressive strength
effective in damping vibrations High resistance to wear
High fluidity at molten state (This permits casting pieces to have
intricate shapes)
Low Cost
Automotive Engine Blocks
Brake discs and drums
Base structure of machines and heavy equipments that are exposed
to vibrations etc.
DUCTILE OR NODULAR CAST IRON
3% to 4% Carbon
1.6% to 2.8% Silicon
Highly ductile
Very good machinability
High Corrosion Resistance
Valves
Pump bodies
Crankshafts
Gears and other automotive and machine components etc
WHITE CAST IRON
1.8% to 3.2% Carbon
0.3% to 1.8% Silicon
Very hard and brittle
Highly wear resistant
No Ductility and Malleability
Not Machinable
Liners for Cement Mixers
Ball Mill
Certain types of Drawing Dies
Extrusion Nozzles etc.
1.8% to 3.2% Carbon 0.3% to 1.8% Silicon
MALLEABLE CAST IRON
Highly Malleable
Very good Machinability
Good Magnetic properties
Wear Resistance
Connecting Rods
Transmission Gears
Flanges
Pipe Fittings
Differential Cases for Automobiles etc.
copper
ALUMINIUM
MAGNESIUM
TITANIUM AND ITS ALLOYS
Copper has
- good thermal and electrical
conductivity
ease of getting cast, machined and brazed
- good corrosion resistance
Pure copper is mainly used for electrical and thermal applications.
ALUMNIUM
Low specific gravity, Corrosion resistance ,
Ease of fabrication,
High electrical and thermal conductivity,
Aircraft structural parts and other highly stressed
applications, Flywheel etc.
MAGNESIUM ALLOYS
for light weight alloys
is relatively soft, and has a low elastic
modulus
APPLICATIONS:
variety of hand-held devices (e.g., chain saws, power tools, hedge clippers),
TITANIUM
has a relatively low density a high melting point
and an high elastic modulus
TITANIUM
extremely strong; tensile strengths are high
the alloys are highly ductile and easily forged and machined.
-airplane structures, space vehicles, surgical implants,
,petroleum and chemical industries.
CERAMICS
metallic and non – metallic elements
with predominantly ‘ionic’ interatomic bonding.
turbocharger
rotors, aerospace turbine blades, nuclear fuel rods,
PLASTICS
thermosetting, and thermoplastic
thermoplastic vs thermosetting
Plastics are synthetic materials processed by heat and pressure.
a solid material consisting of an organic polymer of a long
molecular chain and high molecular weight
THERMOPLASTIC
a polymeric material which softens when heated and hardens upon
cooling.
THERMOSETTING:
a polymeric material, which once having cured or hardened by a
chemical reaction does not soften or melt upon subsequent heating.
A thermoplastic material has a linear polymer chain while a thermosetting plastic material
consists of a cross – linked polymer chain as shown.
THERMOSETTING VS THERMOPLASTIC
The difference in properties of thermoplastic and thermosetting plastic materials is due to
molecular structures of their polymer chains.
what are composites
A composite is a structural material that consists of two or more combined constituents
that are combined at a macroscopic level and are not soluble in each other.
One constituent is called the reinforcing phase and the one in which it is embedded is called
the matrix. The reinforcing phase material may be in the form of fibers, particles, or flakes.
The matrix phase materials are generally continuous.
Examples of composite systems include concrete reinforced with steel and epoxy reinforced
with graphite fibers, etc
elasticity, plasticity,
ductility, Malleability
brittleness,
fatigue
creep
hardness, Impact strenght
static and cyclic load
RESELIENCE
TOUGHNESS
STIFNESS
the ability of the material to regain its shape and size when the externa forces are removed/when deformation occurs
PLASTICITY
ability of material to not to take its shape and size when the external forces are removed
DUCTILITY
ability of the material to be drawn into thin wires when the materials are subjected to tensile
MALLEABILITY
ability of material to deform into sheets under compression load
BRITTLENESS
ability of material
(% elongation is less than 5%) than its brittle material
% elongation (change in L/l)*100
FATIGUE
ability of the material to resist deformation due to cyclic loading
CREEP
it is the function of time and temperature elongated wrt to time
changing shape over time
HARDNESS
ability of the material to resist surface indentation/resistance to penetration
= hardness
BHN= brinal hardness number
VHN=Vekers hardness number
RHN=Rockwells Hardness number
IMPACT STRENGHT
ability of a material to resist the deformation due to sudden load (high magnitude in fraction of time)
charpy test rig
static: magnitude of load doesnt vary with time, cyclic load varies
RESILIENCE V TOUGHNESS
(i) Resilience is the ability of the material to absorb energy within elastic limit and release it,
whereas toughness is the ability of the material to absorb energy within elastic and
plastic range, before fracture. Resilience is essential in spring applications where
toughness is required for components subjected to bending, twisting, stretching and
impact loads.
STIFNESS
the resistance of materials to elastic deformation or deflection its called rigidity,
how much a material resists deformation in response to an applied force. A material with high stiffness will undergo only slight deformation under load
what are smart materials,
Key elements of smart system/structure
Smart materials are materials that have to respond to stimuli and environmental changes and
to activate their functions according to these changes
ELEMENTS OF SMART MATERIALS:
Smart materials are thought of as those which produce electric voltages when strained
ex: Lead Zirconate Titanate, polyvinylidene
fluoride
Sensor
Actuator
Control System
Power and Signal Conditioning Electronics
Computer
PIEZOELECTRIC MATERIALS
By applying mechanical deformations to these crystals, electric dipoles are
generated/pd develops vice versa
in certain class of anisotropic
Voltage and power sources, sensors
SHAPE MEMORY ALLOYS one way and 2 way and examples
The recovery of strains imparted to the material at a lower temperature, as a result
of heating,
alloys shape is fixed/memorised at low temp
ex:
braces, stents
One way: after heating deformation are recovered and cooling = back to same shape
two way: remembers shape at both high temp and low temp ,thus can be cycled btw these 2 shapes without the need of external stress
RHEOLOGICAL FLUIDS
MAGNETOSTRICTIVE MATERIAL ISA(2M)
A special class of fluids exists that change their rheological properties on the application of an electric
or a magnetic field.
MAGNETOSTRICTIVE
materials that change their shape or dimensions in response to an applied magnetic field
stress/strain types
in normal stress list the 2 types
normal stress
(perpendicular): tensile,compression
, sheer load(parallel)
ISA/ESA 2M
plot the graph for mild steel
STRESS- STRAIN DIAGRAM IN COMPRESSION
When the material is compressed, it
bulges outward on the sides and becomes barrel shaped, because friction between the specimen and the end plates prevents lateral expansion.
With increasing load, the specimen is flattened out and offers greatly increased
resistance to further shortening
Brittle materials loaded in compression typically have an initial linear region
the ultimate stresses in compression are much higher than those in tension.
brittle
materials actually break at the maximum load
unlike ductile
draw graph
all the P and V relation and pdV relation
ISOTHERMAL
PV=const, P1V1=P2V2
pdV
W=P1V1ln(V2/V1)
ADIABATIC
PV^a=const, P1V1^a=P2V2^a
pdV
W=(P1V1-P2V2)/a-1
POLYTROPIC
PV^n=const, P1V1^n=P2V2^n
pdV
W=(P1V1-P2V2)/n-1
ISOCHORIC
V=const, dV=0, P1/P2 =T1/T2(Kelvin)
pdV
W=0
ISOBARIC
P=const, dP=0, V1/T1=V2/T2
W=P(V2-V1)
