Topic 3: Thermodynamics

Energy, Heat & Temperature Overview

• Introduction to energy, heat, and temperature concepts.
• Explanation of what energy is.
• Discussion of basic thermodynamics principles.
• Overview of power generation methods.
• Explanation of calorimetry.
• Specific and latent heat concepts.
• Heat transfer mechanisms: conduction, convection, and radiation.

Energy

• Energy is the ability to do work.
• Energy exists in many forms:
  • Mechanical
  • Nuclear
  • Thermal (heat)
  • Sound
  • Light
  • Chemical
  • Electrical
• Principle of Conservation of Energy: Energy cannot be created or destroyed, only converted from one form to another.
• Some forms of energy are more useful than others, leading to the concept of high-grade and low-grade energy based on ease of conversion.
  • Electrical energy is considered "high grade" because it's easily converted.
  • Heat is considered "low grade" because it's harder to convert to other forms.

Terminology

• Heat: Energy transferred from a hotter body to a colder body.
  • A "hotter body" has a higher temperature.
  • There are many ways to increase temperature.
• Work: Energy transferred by the action of a force (e.g., movement of a piston).
• Power: The rate of doing work (Power = Energy / Time).
• Temperature: The "degree of hotness."

Temperature Scales

• Familiarity with Celsius ($^{\circ}C$) but equations use absolute temperature scale in Kelvin (K).
• A change of 1$^{\circ}C$ = 1 K, but different zero-point.
• Temperature scales are calibrated using two fixed points:
  • Pure ice melting: $0^{\circ}C = 273.15 K$
  • Steam: $100^{\circ}C = 373.15 K$
• Absolute zero: $0 K = -273.15^{\circ}C$
• Boiling point of air: $-194.35^{\circ}C = 78.8 K$

Thermal Equilibrium

• When a hot object is put in contact with a cold object, heat flows from the hot to the cold object.
• Heat stops flowing when the two objects are in thermal equilibrium.
• Objects in thermal equilibrium are at the same temperature.
• The 0th law of thermodynamics.

Thermodynamics

• Thermodynamics is about the interaction of a system with its surroundings.
• The system can be a bowl of soup, a cloud, an area of ocean, gas in a cycle tire, etc.
• Thermodynamics deals with processes that cause energy changes as a result of:
  • Heat flow to/from the system.
  • Work done on/by the system.

Internal Energy

• For a gas and a liquid, molecules are moving around.
• For a solid, molecules also move, vibrating within the structure.
• In both cases, they have internal energy.
• Internal energy has two components:
  • Kinetic energy due to the motion.
  • Potential energy stored in the bonds.
• Internal energy can be increased by:
  • Heat flow from a hotter body.
  • Doing work on the system.

Thermal Energy and Absolute Zero

• It is the kinetic energy part of the internal energy (known as thermal energy) which gives rise to the "temperature" of a body
• For a solid, need to think about the internal energy, (internal kinetic/thermal energy) but also about the potential energy within the bonds.
• For a gas within a container, need to think about the motion of the molecules. (internal kinetic/thermal energy)
• At absolute zero, the thermal energy is zero.

1st Law of Thermodynamics

• Internal energy of a system can be changed by:
  • Supplying heat to the system.
  • Doing work on its surroundings.
• $DQ = DU + W$
  • $DQ$ = heat supplied
  • $DU$ = increase in internal energy
  • $W$ = work done by system (on its surroundings)
  • Sign convention: gas expands à +ve $W$, gas compresses à -ve $W$

1st Law in the Environment

• (1) An outcrop of rock warms up during the day. Sun supplies heat ($DQ$ is positive). No work is done because nothing moves, $W = 0$. Therefore, $DQ = DU$. Internal energy increases. The material is solid à more vibration in lattice structure à modest temperature rise (no bonds broken)
• (2) Air mass forced ascent to higher altitude (lower pressure) (e.g., flow over mountain range) -- no heat is supplied/removed ($DQ = 0$) -- air moves to higher altitude à lower pressure.
  • $DQ = DU + W$
  • In this case, gaseous species à air expands (lower pressure) & work is done (higher volume)
  • $DU = - W$ Work done is positive à internal energy decreases
• (2) An air mass descends to lower altitude (higher pressure) (e.g., flow over mountain range) -- no heat is supplied/removed ($DQ = 0$) à work done: air moves to region of higher pressure.
  • $DQ = DU + W$
  • In this case, gaseous species à air is compressed, and work done on the gas (-ve)
  • $DU = - W$ Work done is negative à internal energy increases
• (3) An (absorbing) cloud air-mass is heated by sunlight. It expands, doing work on its surroundings (pushes air out of the way).
  • $DQ = DU + W$
  • $DQ - W = DU$
  • Need to consider whether the heat from Sun ($DQ$ = +ve) is greater than the work done ($W$) on surroundings. Balance of the two ($DQ - W$) determines whether internal energy ($DU$) will increase or decrease, à air temperature in cloud may increase or decrease.

2nd Law of Thermodynamics

• No system can take heat from a source ($DQ$) and convert it completely to useful energy (always some inefficiency à heat).
• Example: a power station cannot burn coal and convert all the heat from burning the coal into electricity.
• Energy is always wasted in conversion.
• (Engineering view of 2nd law of thermodynamics)

Efficiency

• $Efficiency = \frac{useful \ energy \ output}{total \ energy \ input}$
• Examples:
  • Electric motor: ~90% efficient
  • Domestic gas boiler: ~75% efficient
  • Car engine: ~25% efficient
  • Human body: ~50% efficient

Energy Losses

• Energy conversion produces energy losses.
• For energy-efficient design, match the grade of energy supplied to the end-use need.
• Eventually, all energy changes result in low-grade heat - an unavailable form of energy.
• New sources of useful high-grade energy are needed.

Entropy

• Entropy is the measure of the amount of disorder in a substance (relates to statistics = no. of combinations).
• Molecules in a gas move randomly = high entropy.
• Atoms in a crystal (sugar, salt) form a regular pattern = low entropy.
• Water has a higher entropy than ice.
• Internal energy in the form of heat within a gas à random motions of molecules à least ordered state à highest entropy (least order = high disorder = many combinations).
• Entropy determines whether a process is feasible: if $D entropy$ is negative, the change will not occur.
• In a closed system, entropy increases with time (another way to state 2nd Law of Thermodynamics -- but need to understand concept of entropy and initially trickier to conceptualize, (2nd law often stated from engineering perspective).

Examples of entropy and (ir-)reversibility

• Bathroom with hot bath:
  • Hot bath cools down, warming the bathroom in the process, until air and water are lukewarm.
  • Within this closed system the energy is conserved but the entropy increases as the bath cools.
  • The heat cannot be collected from the air and used to heat the bath again, without external energy input.
  • Entropy change Reversibility
• Chemical reactions
  • A chemical reaction will only “go” if there is an +ve entropy change (often also requires energy) à reaction won’t occur if entropy change is negative.

Power generation - Nuclear Energy

• Nuclear Power Plant: Energy efficiency 30-40%

Thermal pollution from power stations

• Huge amounts of cooling water are used to condense the steam back to water for re-use.
• Cooling water may come from lakes/rivers and may be returned to the environment at a higher temperature, with implications for the ecology
• Negative effects include:
  • disrupted spawning grounds
  • less dissolved oxygen
  • increased susceptibility to disease, parasites, toxic chemicals
  • thermal shock may kill fish
• Positive effects include:
  • extended growing season in frost-prone areas
  • increased growth rate of commercial fish & shell fish
  • waste heat can be used

Power Generation

• Power stations use useful high-grade fuel.
• The primary energy source is coal, oil, gas, or uranium.
• About 70% of the energy stored in the fuel is lost during conversion and distribution, half of this is lost via cooling towers.
• Typically, power stations are only ~30% efficient.
• Can think in terms of grade of energy and in relation to change in entropy.

Changes in entropy

• Changes in entropy also explain why energy is transferred when systems move towards a state of thermal equilibrium. For example:
  • Temperature rise of the ocean (or the soil) due to the energy provided from the Sun.
  • Energy transferred when warm and cold air in different weather systems come together.
  • Temperature rise of a river when power plant cooling water is dumped in it.

Entropy – energy conversion

• High-grade (low entropy) forms of energy have more potential to do useful work (feasibility of energy conversion), in a closed system.
  • Electric energy -> Thermal energy (heat) (Conversion highly ineffective)
  • Mechanical energy -> Thermal energy (heat) (Conversion highly effective)
  • Chemical energy -> Thermal energy (heat) (Conversion effective)

Recap: 1st and 2nd laws

• One way to remember the 1st and 2nd laws is to think the 1st law is about quantity of energy and the 2nd law is about flexibility of energy.
• The 1st is the actual equation determining how source of heat to a system do work or increase internal energy (e.g. temperature)
• The 2nd is a more general statement re: changes in the flexibility of energy (grade) à always moves to a state of higher entropy (less ordered state)

Quantitative statement of the 2nd law from a fundamental physics perspective.

• $S=k log W$
  • $S$ = entropy
  • $k$ = Boltzmann’s constant
  • $W$ = number of possible “microstates (re-arrangements) in a system
• Relates to basic statistical properties. Entropy of a system increases with time. Think of entropy in terms of diversity of possible microstates arrangements 2th law of thermodynamics from a fundamental physics perspective.

Notion of “inverted entropy” (film “Tenet”)

• Recent film by Christopher Nolan (Batman Begins etc.) - Concept is that in the future, objects can be changed to travel backwards in time, then having “inverted entropy” and unexpected effects on (or rather “interactions with”) ”normal objects” that are travelling forwards in time.
• A plot within the film sees protagonist changed to be travelling backwards in time (unable to breath ”normal” air) and pursuing villain “Sator” who is also travelling back in time within car-chase scene
• Scene has Sator cause explosion in reverse-time with explosion then removing heat from forwards-air, à part of car windscreen freezes & man gets hypothermia.

Specific heat capacity

• The specific heat capacity is the thermal energy required to raise the temperature of 1 kg of a substance by 1 K.
• $DQ = m C DT$
  • $DQ$ = Thermal energy (or heat) provided (J)
  • $m$ = mass of substance (kg)
  • $DT$ = Temperature change (K)
  • $C$ = specific heat capacity (“Joules per kg per K”) ($J kg^{-1} K^{-1}$)

Some values for specific heat capacity

• Steel 510
• Basaltic rock 1200
• Glass 670
• Ice 2100
• Sand 800
• Concrete 3500
• Air 993
• Fresh water 4190
• Clay 1000
• Sea water 4900
• Hard to reconcile these values at first. Seems counter-intuitive.
• Need to think about gases differently than solids, and liquids
  We will cover the behaviour of gases and liquids later in the module responses to heating and little inter-molecular interactions in gases
• Main thing to understand is that increasing the temperature of a

Example 1

• How much energy does it take to raise the temperature of 1m3 of air by 5 K? (assume no heat losses)
• (Question states that the density of air is 1.2 kg / m3 )
• Apply formula $DQ = m C DT$

Example 2

• 1 liter of water is heated for 10 minutes by a 100 W heater. The container is insulated so there is no heat loss. What is the rise in temperature of the water?
  Set density of water $ρ = \frac{m}{V} ≈ 1 \frac{kg}{l}$

Changes of state

• On heating or cooling, a substance may:
  • melt
  • solidify
  • vaporize
  • condense
  • crystallize
  • sublime
• These changes of state absorb or give out heat without a change in temperature.
• This heat is called the latent heat.
• Change in internal energy doesn’t necessarily cause change in temperature.

Latent heat of vaporisation and evaporation

• Thermal energy $DQ$ required to convert a mass ($m$) of a substance from a liquid to a gas (evaporation) is:
• $DQ = mLv$
  • $Lv$ is the latent heat of vaporization in $J kg^{-1}$
• Additional energy required at the boiling point.
• Liquids of course also evaporate at lower temperatures. (but in that case, it’s only at the surface of the liquid)
• In both cases it’s the same equation, but at lower T has only part of the mass evaporating.

Latent heat of fusion and melting

• Thermal energy $DQ$ required to convert a mass ($m$) of a substance from a solid to a liquid (melting) is:
• $DQ = mLf$
  • $Lf$ is the latent heat of fusion in $J kg^{-1}$

Latent heat in the environment

• It is required to answer questions like:
  • How much polar ice will melt if the temperature of the earth rises by $1^{\circ}C$
  • How much sea-level will rise if the temperature of the earth rises.
  • How much solar energy is needed to vaporize a certain volume of ocean and put it into the atmosphere

1st Law in the Environment (revisited)

• (1) An outcrop of rock warms up during the day. Sun supplies heat ($DQ$ is positive). No work is done because nothing moves, $W = 0$. Therefore, $DQ = DU$. Internal energy increases. The material is solid à more vibration in lattice structure à modest $T$ rise … no change in state/phase (T below the melting point of the rock!)
• (1) A lump of ice exposed to the Sun. Sun supplies heat ($DQ$ is positive). No work is done because nothing moves, $W = 0$. $DQ = DU$ Internal energy increases. The material is solid à more vibration in lattice structure à increase in T … in this case not only does T increase, but also

Heating ice / water / steam

• At $0^{\circ}C$, heat is being transferred to the ice block but its temperature does not increase. Internal energy is changing because of changes in state.
• Water: $Lf = 3.3 \times 10^5 J kg^{-1}$, $Lv = 2.3 \times 10^6 J kg^{-1}$

1st Law in the Environment (3)

• An (absorbing) cloud air-mass is heated by sunlight. It expands, doing work on its surroundings (pushes air out of the way).
• $DQ = DU + W$
• $DQ - W = DU$
• Need to consider whether the heat from Sun ($DQ$ = +ve) is greater than the work done ($W$) on surroundings à air temperature in cloud may increase or decrease
• Something not quite right in this statement. Didn’t consider evaporation/condensation in the cloud

Example 3

• A dish contains 1kg of water. How much energy is required to evaporate 10g of the water? How much does this cool the remaining liquid water assuming no heat exchange with the atmosphere?
• Apply 1st law of thermodynamics (with no work done)
• Part 1 – heat energy required to evaporate 10g of water
• Part 2 – how much does this removal of heat cool the remaining liquid phase water?
• Hint – You will need to find the latent heat of vaporisation and the specific heat capacity of water from the preceding slides.

Example 4

• Ice-cube tray with 50g of water at 20oC is put in the freezer. How much energy is applied if the ice is then at -5o C? Again, apply 1st law of thermodynamics (with no work done)
• Part 1 – heat energy exchanged to cool the 50g water 20à0oC
• Part 2 – heat energy exchanged to change 50g water à ice
• Part 3 – heat energy exchanged to cool 50g of ice 0oC à -5oC
• Hint – You will need to find latent heat of fusion of water and specific heat capacity of water & ice from preceding slides.

Heat transfer mechanisms

• As well as changes to internal energy, we also need to think about how thermal energy is transferred. It will help us to understand:
  • movement of heat in the atmosphere and oceans
  • how energy from the Sun gets to Earth
  • heating of rocks / soil / water to different depths
  • how to prevent heat losses from buildings
• Three heat transfer mechanisms:
  • conduction
  • convection
  • radiation

Conduction of heat

• Example: metal spoon in pan of hot soup
• Heat is transferred because of temperature differences between parts of the spoon
• Atoms and molecules at the ‘hot end’ have more internal energy so vibrate more
• Neighboring atoms are caused to vibrate à sets their neighbors vibrating à T rises even though not directly heated
• The medium does not move
• Depends on properties of the substance -- some materials can be good or poor thermal conductors

Convection of heat

• Example: a radiator heating a room
• Heat is transferred by movement of a fluid in a gravitational field
• Hotter, less dense air (near radiator) rises
• Cooler, denser air near ceiling is displaced downwards
• Convection currents are set up
• Very important in the atmosphere and oceans
• Hard to predict nature of convection à can be in organized cells or more turbulent motion.

Convection in the atmosphere

• Earth receives more energy at the equator than the poles
• Hot air at the equator rises à then meridionally (North/South from equator) à cools and descends ~30N/S
• These convection cells are known as “Hadley cells”
• Leading mode of variability for meteorology at low latitudes

Radiation of heat

• Example: energy from the Sun
• Energy is transmitted by electromagnetic waves
• No medium is needed - radiation can occur through a vacuum
• Very fast energy transfer - radiation travels at the speed of light

Radiation of light : “red hot” & “white hot”

• Bulb designed for filament to reach the very high temperatures to “glow” whilst glass heats up only to ~100-160oC (373- 433K).

Thermal conductivity - equation

• Thermal energy conducted per s “Heat transfer rate” is given by $\frac{DQ}{Dt}$, with units $Js^{-1}$ à i.e. in Watts
• $\frac{DQ}{Dt} = -k A \frac{DT}{Dx}$
  • $\frac{DT}{Dx}$ = thermal gradient
  • $A$ = cross-sectional area of the material
  • $k$ = thermal conductivity of the material in $W m^{-1} K^{-1}$
  • $Dx$ = thickness of material (in the direction of the heat transfer)

Thermal conductivity problems

• In example sheets and exams, problems usually deal with heat flow (or heat flux) through successive layers of material, the transfer of heat at right angles to the layer.
• A key part of the calculation is the area of material through which the heat is flowing
• Some questions will involve amount of heat that flows into the layer = amount of heat that flows out - so there is no change in internal energy (e.g. no rise in temperature).

Thermal conduction and change in internal energy

• However, sometimes a heat flux into the material is not equal to the conduction heat flux out. (there is a change in internal energy)
• Flux convergence à net heat transfer is +ve à increase in internal energy à +ve DT (or melt)
• Flux divergence à net heat transfer is –ve à decrease in internal energy à -ve DT (or freezing)

Thermal conduction in the soil

• Conduction through the soil depends on soil type and wetness
• When vertical flux convergence and divergence occurs in soil layers à warming or cooling à progression in T-profile within soil through the day/night.

Some values for thermal conductivity

• Materials with low thermal conductivity are good insulators à means the conduction heat flux through the material is slow.
• Steel 12.1 - 45.0
• Sandstone 1.83 – 2.90
• Glass ~1.0
• Ice 2.3
• Air 0.026
• Concrete 0.8 – 1.28
• Soil (dry) 0.15 – 2.0
• Fresh water 0.6
• Soil (wet) 0.6 – 4.0
• Snow 0.05 – 0.25

Example 5: Thermal conductivity

• The end of a metal rod is dipped in a bucket of ice at 0oC. You hold the other end of the rod, which is at a T= 25oC. The rod has a radius of 5 mm and a length of 30cm. If the thermal conductivity of the metal is $20 W m^{-1} K^{-1}$, What is the rate at which heat flows from your hand to the ice (assuming no heat loss to the air)
• Hint: First find the cross-section area of rod. Then apply the conductivity equation $\frac{\Delta Q}{\Delta t} = - k A \frac{\Delta T}{\Delta x}$

Insulating buildings

• Aim: to reduce heat losses (conduction, convection, and radiation)
  • Double glazing
  • Loft insulation
  • Cavity wall filling
• Builders / architects talk about “the U value” of a material. Although this looks similar to the thermal conductivity equation it includes all heat transfer for the whole material, (not just conduction). (e.g. to quantify the insulation from a double glazing unit.)
• $\frac{DQ}{Dt} = -U A DT$
  Consider overall transfer of heat from warmer indoors à cooler outdoors

Example 6: Cavity wall filling

• A brick cavity wall has a U value of $1.6 W m^{-2} K^{-1}$. A house has an external wall area of $35 m^2$. What is the heat loss through the walls if it is 21oC inside and 4oC outside? What difference would cavity wall filling make to heat loss rate? (${U1} = 0.5 W m^{-2} K^{-1}$).
• $\frac{\Delta Q}{\Delta t} = - U A \Delta T = - 1.6 W m^{-2} K^{-1} \times 35 m^2 \times (4 K – 21 K) = 952 W$
• $U2 = 0.5 W m^{-2} K^{-1}$ à heat loss = 298 W, factor of 3 less ($\frac{U1}{U2}$).

Summary

• Energy and temperature
• Thermodynamics (the 1st and 2nd laws of thermodynamics)
• Introduced the concept of entropy
• Changes in internal energy
• Latent heat, specific heat capacity
• Heat transfer
• Conduction, convection, radiation