Thermodynamics: Energy, Heat Transfer and Work

Thermodynamics Summary

• Energy is a universal property capable of causing change; work is done through force application.
• Stars radiate internally developed energy, which can be absorbed by planets at suitable distances.
• Heat is a form of energy and its production/release can perform work and it is defined as thermal energy is the application, loss, or transfer of heat.
• Thermal energy cannot be created or destroyed but can be converted into and from electrical, chemical, mechanical, or nuclear energy.
• Gases easily absorb and radiate heat energy and convert it into useful work, and is a basic propulsion principle.

Heat Transfer

• Conduction involves physical contact between bodies with different heat levels.
• Hot material molecules transfer energy to colder material molecules.
• Energy transfers internally from molecule to molecule within a heated body due to agitation and temperatures equalize before heat loss.
• Cooling fins on an engine cylinder remove heat through conduction.
• Gasoline combustion in a cylinder releases heat that is conducted to the cylinder head and cooling fins, then to the cooler air.
• Convection is the process of heat transfer through the bulk movement of a fluid.
• Fluid that is being heated becomes less dense and rises, being replaced by cooler fluid.
• Examples of convection include heating water in a kettle, heating air in a house, and atmospheric heat circulation.
• Handles of saucepans are made of materials with low heat conductivity to stay relatively cool.
• Electromagnetic radiation (EMR) is energy emission from object surfaces due to charged particle acceleration.
• EMR involves periodic variations of electric (E) and magnetic field (M) strengths caused by accelerating charged particles.
• Charged particles within molecules constantly change direction, causing acceleration.
• M and E waves are perpendicular, non-mechanical, and able to travel through the atmosphere or a vacuum and around 1013 Hz, wave motion propagates energy as heat (infrared).
• The sun radiates energy across 93,000,000 miles of vacuum, which is radiant heat, with conduction and convection occurring slowly, while radiation occurs at light speed.

Kinetic Theory of Matter

• Molecules constantly are in random motion, associated with kinetic energy as heat.
• Increased heat results in faster molecule movement and substance changes.
• Solids contain particles in a lattice structure, liquids contain particles that roll, and gases contain quickly moving particles.
• Kinetic energy causes particle movement in all states, and solids expand due to increased molecular space, and is why railway tracks and bridges have expansion joints
• Linear Expansion Formula: E = kL(T2 - T1)
  • k = coefficient of linear expansion for the material
  • L = original size
  • (T2 - T1) = temperature difference
• Bimetallic strips, made of two dissimilar metals, expand differently when heated, causing stress and bending with temperature variation.
• Bending bimetallic strips operate electrical contacts in thermostats and regulate clock wheel balance.
• Adding heat causes substances to change state from solid to liquid, and then to gas, and with enough heat the molecules become independent of each other.
• Transferring energy as heat can induce change, which is easily observed in incompressible solids and liquids.
• Behaviour of gases as they absorb and release heat must be examined to understand how gases help create propulsion.

Units of Heat

• Calorie (cal): The heat to raise 1 g of water by 1 °C.
• British thermal unit (Btu): The heat to raise 1 lb of water by 1 °F.
• Joule (J): The SI unit for all forms of energy where 1 J of energy can do 1 J of work.
• Heat Produced: Burning 1 liter of gasoline produces ≈ 8 × 10^6 cal, 3 × 10^4 Btu, or 3 × 10^7 J (30 MJ).

Specific Heat

• Temperature signifies the degree of heat one mass possesses over another.
• Heat flows from the hotter to the cooler body.
• Specific heat and heat capacity are defined due to differing heat content with Temperature, for example a cup of water at 90°C contains less heat than a swimming pool at 20°C.
• Specific Heat: Joules of heat needed to raise 1 gram of a substance by 1 K. Water requires 4 joules to raise 1 gram by 1 K.
• Smaller energy raises the temperature of metals more than water.
• 4 joules raises the temperature of 1 gram of copper by 11 K with Specific Heat ≈ 1/11 of water's value or 0.0923.
• Oceans' temperature is consistent due to water's high specific heat as temperature is less impacted by the change of seasons compared to land.
• Heat capacity is the amount of heat needed to change an object's temperature by one Kelvin, measured in J/K, determined by composition and mass.
• To solve for heat required, mass and specific heat need to be known and is the number of joules required to heat 1 kg of the object's mass by 1 K with the measurement of JK⁻¹kg⁻¹.
• Equation to solve heat required: m * c * Δ
  • Q = heat energy supplied (J)
  • m = mass (kg)
  • c = specific heat capacity (J K⁻¹ kg⁻¹)
  • Δ = temperature change (K)

Temperature Scales

• Temperature scales are represented as the average kinetic energy of molecules in degrees (°).
• Four main temperature Scales
  • Degrees Celsius (°C)
  • Degrees Fahrenheit (°F)
  • Kelvin (K)
  • Rankine (°Ra).
• The Kelvin scale does not use the degree symbol (°) The boiling point for water is 373 K.
• Thermometers use consistent state changes to measure temperature.
• Change of state does not expand a substance so mercury expands and contracts between fixed melting ice and boiling water to relate between different temperature scales.
• Celsius Scale: The melting point of pure ice is 0°C and water’s boiling point being100°C and is divided into 100 increments.
• Kelvin Scale: This ranges between the freezing and boiling points of water, but zero is absolute zero (-273.15°C).
• Equations to convert between Kelvin and Celsius scales:
  • K = °C + 273
  • °C = K - 273
• The Fahrenheit scale has 180 increments and the freezing point of water is 32°F and boiling point is 212°F.
• Equations to convert between Celsius and Fahrenheit
  • °F = 9/5 °C + 32
  • °C = 5/9 (°F - 32)
• The Rankine scale is the Fahrenheit equivalent of the Kelvin scale.

Latent and Sensible Heat

• Mercury thermometers measure substance temperature in Celsius, Kelvin, etc., not heat energy in joules.
• Sensible Heat: Heat added/removed to change water's temperature.
• When water boils at 100°C and is converted to water vapour or steam the thermometre remains constant and the steam is also 100°C.
• As State Changes to Steam: The thermometer doesn't expand/contract but it adds heat/joules.
• Latent Heat: Heat causes a substance to change state without changing temperature and breaks down intermolecular bonds but does not increase temperature.
• Heat of Vaporization: Heat to boil/vaporize liquid.
• Heat of Fusion: Heat to melt a solid.
• Sensible heat is stored in intermolecular forces with increasing it increasing the kinetic energy of the molecules.
• Heat lost (dissipated) causes opposite state changes like vapour to liquid (condensation) at 100°C and/or liquid to ice (freezing) at 0°C with the latent heat of vaporisation and fusion respectively.
• 1 gram of water gains 540 calories of heat during change from 100 °C water to steam at 100 °C.
• 1 gram of steam loses 540 calories of heat during change from steam at 100 °C to liquid water at 100 °C.
• 1 gram of water gains 100 calories of heat during change from 0 °C water to 1 g of water 100 °C (sensible heat).

Latent Heat and the Refrigeration Cycle

• Refrigerant gas condenses into liquid at high pressure where compression heats refrigerant.
• Heat is dissipated through coils.
• The liquid refrigerant flows through the expansion valve.
• The liquid refrigerant immediately boils and vaporises using its own latent heat, dropping temperature to -27 °F (-33 °C) making the refrigerator cold, and cycle repeats.

Air Conditioning

• Cold Cycle:
  • Refrigerant evaporates to cold gas using latent heat inside and condenses to a liquid, giving off heat to air, outside.
• Reverse Cycle (Heat Pump):
  • Refrigerant evaporates to cold gas using latent heat, extracting heat from air outside and condenses to a liquid, giving off heat to the room.

Gas Laws

• Gases versus Solids and Liquids: Gases are compressible, affecting how forces are transmitted and used to do useful work.
• The work by an expanding gas in an engine exemplifies examining compressed confined gases being put under temperature and pressure changes.
• As gas is compressed the pressure increases and volume decreases, assuming temperature remains constant and the molecules are contained in a smaller area
• If volume is halved then pressure doubles due to compression, but temperature stabilizes
• Boyle's Law: Volume of gas varies inversely with pressure at constant temperature.
  • V1 / V2 = P2 / P1
• Isothermal Process: A process taking place at a constant temperature with gases.
• Charles's Law: The volume of a gas varies in direct proportion to its temperature, assuming pressure remains constant
  • V1 / V2 = T1 / T2
• Heating Gas: Heating gas will cause it to cause the container to increase in size and doubling temperature double volume
• Gay-Lussac's Law: Volume is constant which uses temperature and pressure values, bottles left out in the sun could over-pressurise and need relief valves.
  • P1 / P2 = T1 / T2
• Adiabatic Process: Temperature change without external heat addition/removal, for example increase in cylinder temperature when the fill rate is high.
• General Gas Laws: Describes what happens when the container is flexible and P, T and V changes simultaneously and combines Boyle’s and Charles’ laws, where temperatures and pressures must be absolute to avoid negative values.
• (P1 * V1) / T1 = (P2 * V2) / T2

Thermal Energy

• The first of thermodynamics is similar to the law of conservation of energy: "Heat energy cannot be destroyed; it can only be changed from one form of energy to another."
• Heat is transformed into mechanical energy but some energy is transformed to sound energy due to losses or inefficiencies
• The second law of thermodynamics states that heat flows from a warmer body to a cooler body and is used in car radiators, heat exchangers/oil coolers.
• Anytime fuel is burnt (combustion), heat is produced. The heat can be useful and/or unwanted.

Heat of Combustion

• Combustion produces heat and uses liquid solid or gas fuels for a range of purposes.
• With Combustion Engines: Wasted heat needs dissipation to optimize engine operation.
• Water is used to circulate around and cool a radiator, circulating around engine and allowing its temperature to remain within a specified range.
• Without regulation, build up is dangerous
• In gas turbine (jet) engine needs to be put under compression to allow work while flowing it
• Higher gas volume in turbine section drives turbine and contributes to reactive thrust
• It is important to monitor gas turbine engines to observe maximum operating temperatures as materials construction cannot withstand high temps.
• Expanding Gas: Some combustion's main purpose is hear expansion
• The heat increases the gas and makes the bullet be pushed out the barrel when a gun is fired.
• With turbine engines gas expands driving the turbines making thrust with mechanical processes.
• Work is calculated by multiplying force applied by distance: Work = Force × Distance with the greater force applied to an object the more work is done.
• Formula: W = F × d = 10000 × 0.5 = 5000 J
  • (10 000 is in the force applied from the rifle)

Heat Engine Gas Cycles

• Gas Cycle Definition: Compressing a gas reduces space between molecules but their total count stays but the collisions increase .
• The is the increased kinetic activity which then increases temperature in the gas being compressed.

Engine gas cycles

• In turbine/piston engines, compressing air is needed before introducing and igniting fuel and significantly raises the temperature of it the air.

Piston Engine (Otto Cycle)

• Reciprocating motion turns into rotary motion to drive a propeller in a four cycle operation

Parts of the Piston:

-Intake: Air and fuel are sucked into the cylinder through the intake valve.

• Compression: Mixture (15:1) is compressed adiabatically into a smaller volume.
• Power: Spark plug ignites the compressed mixture and the hot gas is expanded and cools adiabatically.
• Exhaust: exhaust gases are forced out from the valve as the piston ascends.
• More strokes are increased with multiple cylinders

The gas turbine cycle

• Turbine engine cycles develops power to the following graph

Pressure

• 4 to 5: Power Stroke Intake, Compression, Combustion, Exhaust
  • The work amount is the area of the closed graph, and therefore power = work / time. Because the combustion portion of the cycle occurs when the volume stays the same amount, (3-4 on the graph), the piston engine follows a constant volume engine.

Gas Turbine Engine: The Brayton Cycle

• Gas Turbine Engines compress a mixture of air and fuel, burning releasing Energy
  • Intake: Air is drawn in the front of the cycle
  • Compression: Air is squeezed by a series of compressing fans.
  • Power: Fuel is added to combustion area, igniting through start procedure; Fuel is burning constantly with compressed air. The turbines connected back to the compressor and that helps rotate and continually supply air for combustion which is ~50% leaving plenty to provide Thrust Turbocooling
• Exhaust: Hot gases leave engine in through shaped duct providing providing air to the mass of heat to originally mass intake

Turbine Engine

• Turbine engines use pressures to show that the volume / engine
  • Pressure is equal to each of the volume for the gas turbine stage
• The Combustion happens at constant, hence constant pressure cycle
• The Turbocooling occurs at roughly the same stage Thrust Jetting Process
• Turbo Jet cycle: All thrust is delivered via the Exhaust

Engines

-Turboprop: extra turbin transfer the power output through the shaft propeller

• Turbine Fan: Extra turbin transfer power via air mass -Turboshaft: These all transfer the power to deliver applications to power electrical generators shippings and helicopters rotor

Development of Thrust

Formula: F = m * (V – U) / t Which can be written F = m/t * (V – U) Where m/t = mass flow rate of air in kg/s.

• U = air initial velocity as it enters the engine.
• V = the velocity at which the exhaust leaves. Air to Propeller: A big amount of air acceleration with jet and it provides a smaller mass acceleration with a large acceleration.