Thermodynamics and Engines

• First law of Thermodynamics:

  • Describes the conservation of energy in a system where energy can be transferred through doing work or heating.
  • The energy trasnferred to a system through heating is equal to the sum sum of the increase in internal, energy and work done by the system.

  $Q=$$\Delta U+$$W$

  
• Importance of Q:

  • Q is the energy transferred to the system through heating.
  • If Q is negative, energy is transferred away from the system through cooling.
• Importance of W:

  • This is the work done by the system and occurs when a gas expands.
  • If W is negative, a gas is being compressed as heat energy is being transferred out of a system.
• Internal Energy:

  • The internal energy (U) of a system is equal to the sum of all of the kinetic energies and potential energies of all its particles.
  • As ∆U represents the increase in internal energy, if ∆U is negative the internal energy will decrease.
• Open Systems:

  • This is where gas can flow in, out or through the system therefore gas can cross the boundaries of the system.
  • An example of an open system is in an aerosol can.
• Closed Systems:

  • This is where no gas can leave or enter the system, but boundaries of the system may cahnge when the gas changes volume.
  • An example of a closed system is the air inside a balloon.
• Applications of the first law of thermodynamics:

  • Can applied to human metabolism, where Q would be negative as the human body expels heat to its surroundings.
  • W is positive as work is being done by the body.
  • The diagram shows that the internal energy of the body as ∆U must be negative to make the equation below accurate.

  
• Non-flow processes:

  • These are changes that occur in closed systems as gas doesn't flow across boundaries.
  • In order for first law of thermodynamics to apply, the gas must be ideal.
• Ideal gases:

  • These are gases that have no other interaction other than perfectly elastic collisions between molecules, which means that no intermolecular forces act between molecules.
  • An ideal gas has no potential energy, so its internal energy is equal to the sum of the kinetic energies of all its particles.
• Adiabatic Processes:

  • These occur when no heat leaves or enters the system, there for Q=0.
  • Using first law of thermodynamics, it is seen that increase in internal energy is equal to the work done by the system: $\Delta U=$$-W$.
  • For adiabatic change, the product of pressure and volume to the power of the adiabatic constant is constant: $pV^\gamma=$$constant$.
• Isothermal Processes:

  • This is where the temperature of the system remains constant, therefore ∆U = 0.
  • Using first law of thermodynamics, the energy transferred to the system through heating is equal to the work done by the system: Q = W.
  • The product of pressure and volume is constant, therefore the process obeys Boyle's Law: pV = constant.
• Requirements for Isothermal Processes:

  • Take place in a container that is a good conductor.
  • The process is slow.
  • If the system is being heated, the work done by the system will equal the energy transferred to the system.
  • If the system is cooled, the work done on the system will be equal to the energy transferred from the system
• Isobaric Changes:

  • Pressure of a system remains constant.
  • Work done can be calculated by using the formula: $W =$$p\Delta V$.
  • Heating a gas at a constant pressure will cause it to expand, the change in volume and work done by the system are positive.
  • Cooling a gas at a constant pressure will cause it to be compressed, the change in volume and work done by the system are negative.
• Isochoric Changes:

  • A constant volume change is where the volume of the system remains constant, therefore W = 0 as no work is done by or on the system.
  • Using the first law of thermodynamics, it can be seen that the energy transferred to the system is equal to the increase in internal energy: $Q =$$\Delta U$.
  • If heated, the temperature will increase whereas it will decrease if the system is cooled.
  • The entire value of energy transferred is used to heat or cool the system.
• p-V Diagrams:

  • These can be used to represent non-flow processes, and an arrow is used on the graph to indicate the direction of the change.
  • Work done can be estimated by counting squares or by the Trapezium method.
• Adiabatic p-V diagram:

  • No energy is transferred in or out of the system.
  • Adiabatic compressions does more work than isothermal as area under graph is larger.

  
• Isothermal p-V diagram:

  • The temperature of the system is kept constant.
  • The graphs are known as isotherms.
  • The higher the temperature, the further the curve is from the origin.

  
• Constant Pressure p-V diagram:

  • The pressure of the system is kept constant.
  • This is also known as an isobaric change.
  • The work done by the process can be calculated using: $Work =$$P\Delta V$.

  
• Constant Volume p-V diagram:

  • The volume of the system is kept constant.
  • As the curve is a straight vertical line, it has no area so no work is done by this process.
  • Also known as an isochoric change.

  
• Cyclic Processes:

  • This is where the system undergoes two or more processes one after another and returns to its initial volume, temperature and pressure.
  • The p-V diagram for these processes forms a loop.
  • Work done is the difference between work done on the system and work done by the system.
  • Therefore, work done per cycle is the same as the area of the loop.
  • These processes can be repeated continuously, meaning they could potentially release a large amount of energy.
• Internal Combustion Engines:

  • These contain cylinders of air which form systems.
  • The air within the cylinders is compressed when the engine is at a low temperature and expanded when it is at a high temperature.
  • As less energy is required to compress the air at a low than the amount of energy released when the gas is expanded at a high temperature, there is a net energy output by the system.
• Four Stroke Engine - Induction:

  • The piston moves down, causing volume to increase and a mixture of petrol vapour and air is drawn in.
  • It is drawn in through an open inlet valve. The pressure of the gas remains constant, and is just below atmospheric pressure.
• Four Stroke Engine - Compression:

  • The inlet valve is closed and the piston moves up, doing work on the gas, causing its volume to decrease and its pressure to increase.
  • Near the end of the stroke, the spark plug creates a spark which ignites the gas mixture.
  • This causes the temperature and pressure to increase dramatically at a near constant volume.
• Four Stroke Engine - Expansion:

  • The gas mixture expands and so does work on the piston, causing it to move down the cylinder.
  • As the gas is now at a higher temperature, the work done by the gas is higher than the work used to compress it.
  • Near the end of the stroke, an exhaust valve opens and the pressure reduces to near atmospheric pressure.
• Four Stroke Engine - Exhaust:

  • The piston moves up the cylinder, forcing the burnt gas out of the cylinder through the open exhaust valve. The pressure stays at slightly above atmospheric pressure.

  
• Differences between Diesel and Petrol Engines:

  • Ignition is the main difference between a diesel and petrol engine.
  • Gas and petrol is ignited by a spark before the end of the compression stroke so there is enough time for the ignition to complete before the piston finishes its stroke.
  • In a diesel engine, only air is drawn into a cylinder. Fuel is injected via direct injection into the cylinder.
  • The diesel is compressed and temperatures rise, where it will be ignited by the increase in temperature caused by rises in pressure and heat from the glow plug.
• p-V diagrams for engines:

  • Also known as indicator diagrams.
  • These can be used to calculate output power and efficiency of an engine.
  • Theoretical Diagrams:
  • Same gas is constantly moving through the cycle.
  • Pressure and temperature can change instantaneously.
  • No friction is experienced by engine.
  • Heat source is external.
  • Actual:
  • Formed using recorded data.
• Four-stroke Petrol p-V diagram:

  A-B - The gas is compressed adiabatically.

  B-C - Heat is supplied, volume is kept constant.

  C-D - The gas expands adiabatically (and therefore cools.)

  D-A - The system is cooled at a constant volume.

  
• Four-stroke Diesel Engine:

  • A-B - The gas is compressed adiabatically.
  • B-C - Heat is supplied, pressure remains constant.
  • C-D - The gas expands adiabatically (it cools).
  • D-A - The system is cooled at a constant volume.

  
• Actual p-V diagrams for petrol and diesel engines:

  • Key differences:
  • Actual diagrams have rounded edges because the valves in the engine take time to open and close, so the same air is not used continuously as assumed.
  • In petrol engines, heating does not occur at a constant volume as is requires instantaneous increases in temperature and pressure.
  • Actual diagrams highlight negative work done by the engine, shown by the small loop between the induction and exhaust lines.
  • Theoretical diagrams have higher peaks as it is assumed an external heat source causes higher pressures.

  
• Indicated Power:

  • The net work done by the engine each second or simply the power developed by the engine.
  • Calculated by the number of cycles occuring in the engine per second: $Number\:of\:cycles\:per\:second =$$\frac{1}{Time\:for\:one\:cycle}$.
  • The indicated power for a single cylinder is the area of the main p-V loop.

  Indicated Power = (area of p-V loop) x (no. of cycles per second) x (no. of cyclinders)
• Brake and Friction Power:

  • Brake power is the power output by the engine.
  • Friction power is what must be used to overcome frictional forces within the engine.

  Brake Power = Indicated power - friction power.Friction Power = Indicated power - brake power.

  Brake power can also be found using: $P=$$T\omega$
• Input Power:

  • Input power can be calculated by finding the product of the calorific value of the fuel and its flow rate.
  • Input Power = Calorific Value x Fuel Flow Rate.
• Engine Efficiencies:

  • Overall efficiency - the overall efficiency of the engine (the product of thermal and mechanical efficiency.) $Overall\:efficiency =$$\frac{brake\:power}{input\:power}$.
  • Thermal efficiency - A measure of how efficiently the chemical energy from the fuel is transformed into work. $Thermal\:efficiency =$$\frac{indicated\:power}{input\:power}$
  • Mechanical Efficiency - Depends on the amount of energy lost due to moving parts in the engine. $Mechanical\:Efficiency =$$\frac{brake\:power}{input\:power}$
• Second Law of Thermodynamics:

  • A heat engine must have both a source and a sink to operate.
  • The engine must be heated by the source and it must lose a part of the energy it gains to the sink.
  • Heat engines cannot be 100% efficient.
• Heat Engines:

  • $Efficiency=$$\frac{W}{Q_H}=$$\frac{Q_H-Q_C}{Q_H}$.
  • $Maximum\:theoretical\:efficiency =$$\frac{T_H-T_C}{T_H}$
  • Using above equation, it can be seen that a heat engine is only 100% efficient once the cold sink has a temperature of absolute zero.

  
• Comparisons of theoretical and maximum efficiencies:

  • Real efficiencies are usually much lower than their theoretical maximums.
  • Work must be done in order to overcome the frictional forces in the engine.
  • The fuel is not completely burned, so temperature is not as high as theoretical maximum.
  • Power is used to drive internal components of the engine.
• Reversed Heat Engines:

  • These have work done on them in order to transfer energy from a colder region to a warmer one.
  • Often have two forms:
  • Refrigerators - Extract as much energy from the cold region as possible for each joule of work done.
  • Heat pumps - Transfer as much energy to the hot region as possible for each joule of work done such as heating a house.