Ideal gas – model assumptions:

• Volume of a gas molecule is much smaller than the gas volume

→ gas molecules are material points

• Range of forces between two interacting molecules is much smaller

than an average distance between molecules

→ intermolecular interactions are negligible and molecules move in

straight lines between collisions

• Collisions between molecules are perfectly elastic (i.e. no loss of

energy)

Pressure p is a physical value equal to the

force acting on a surface of the body along

the normal direction to that surface:

p = dFn / dS

where: Fn is the normal force acting on dS

Unit of p: 1 pascal; 1 Pa = 1N / 1m2

Temperature

Absolute temperature - defined as a value

proportional to the average kinetic energy of particles:

T=2/(3k)*(mv2/2)

where: k = 1.38·10 - 23 J / K is the Boltzmann

constant

Unit: 1 kelvin (K)

Equation of state of an ideal gas

After transformations:

pV = NkT or: pV = nRT

where: n - number of moles of gas

R = 8.3145 J/(mol·K) – gas constant

NA = 6.023·10 23 mol-1 - Avogadro constant

(numebr of gas molecules in 1 mole)

R = kNA

Principle of thermal equilibrium

„0” thermodynamic law

If the bodies 1 and 2 are in thermal equilibrium and

bodies 2 and 3 are in thermal equilibrium thus bodies

1 and 3 are in the same thermal equilibrium

_ mean kinetic energies of molecules of two gases

in contact are equal

3. Principle of equipartition of energy

Mean kinetic energy per one degree of

freedom is the same for all molecules and

equals to kT/2.

• Energy is distributed uniformly over degrees of

freedom

Total kinetic energy of a molecule (treated as a rigid

body) is:

E=f/2*kT

For N-particle system – internal energy U:

U=Nf/2*kT

4. First law of thermodynamics

Heat absorbed by the system is equal to the increase of

internal energy of the system and the work performed by

the system on the surroundings.

ΔQ = ΔU + ΔW

HEAT ΔQ – energy exchanged between the system

and surroundings due to temperature difference

HEAT and WORK

Energy transfer – as a heat Q or work W (by means of the

force acting on the system)

Q and W – not a property of the system (contrary to T, p and V)

Thermodynamic process:

Initial state P (pp, Vp, Tp) → final state K (pk, Vk, Tk)

INTERNAL ENERGY

Difference ΔQ – ΔW = ΔU is the same for all processes !

U – the function of state,

contrary to Q and W

Internal energy of the system U

- increases when it takes energy in a form of heat Q

- decreases when it performs work W

Unit of U, Q, W: 1 joule (J)

5. Heat capacity of a system C – the quantity of

heat required to rise the temperature of a body through

one degree 1K (1 0C)

Specific heat capacity c – heat capacity per unit

mass: dQ = M c dT

Molar heat capacity Cm – heat capacity of unit

amount of substancje: Cm=1/n*dQ/dT

6. Isothermic process

p ⋅V = n ⋅ R⋅T

If T = const

p1*V1=p2*V2

Isobaric process

p ⋅V = n⋅ R⋅T

If: p = const

V1/T1=V2/T2

Isochoric process

If: V = const

p1/T1=p2/T2

7. Second law of thermodynamics

Question: is it possible to build a machine which

takes heat and transform it fully into work?

1) Perpetum mobile of second type (self-acting

machine) can not be constructed

2) When two bodies with different temperatures are in

contact, then the heat flows from the body with higher

temperature to that with lower temperature

→ directional process

3) Efficiency of every cyclic machine working between

temperatures T1 and T2 is not higher than (T1 - T2) / T1.

ENTROPY

Entropy is a measure of the system disorder

→ The larger disorder of molecule position and velocity,

the higher probability that the system will be in that state.

 2nd law of thermodynamics –

related to entropy

1st law of thermodynamics

– related to internal energy

 ”0” law of thermodynamics

– related to temperature

Carnot cycle

→ determines the limit of possibility of transformation of heat to work

(1) Gas state is p1, V1, T1 (point A). Cylinder is placed on the heat

pump → thermal expansion of gas to state p2, V2, T1 (point B). Gas

absorbs heat Q1.

(2) Cylinder is placed on the insulation → adiabatic expansion of gas

to state p3, V3, T2 (point C). Gas performs the work during moving the

piston and temperature decreases to T2.

(3) Cylinder is placed on the refrigerator (T2) → isothermal compression

of gas to state p4, V4, T2 (point D). Gas gives heat Q2 to the refrigerator.

(4) Cylinder is placed on the insulator → adiabatic compression of gas to

state p1, V1, T1 (point A). External forces perform work and temperature

of gas increases to T1.

8. The mechanisms of HEAT TRANSFER

• Conduction

• Convection

• Radiation

Conduction – energy transfer from

the more energetic particles of a

substance to the adjacent less

energetic ones → a result of

interactions between the particles.

Convection - energy transfer between

a solid surface and the adjacent liquid

or gas which is in motion → it

involves combined effects of

conduction and fluid motion.

Radiation - energy emitted by matter

in the form of electromagnetic waves

(or photons) → a result of the changes

in the electronic configurations of the

atoms or molecules.

9. CONDUCTION

The rating problems deal with the determination of

the heat transfer rate for an existing system at a

specified temperature difference.

Q= dQ/ dt (J/s = W)

Heat transfer rate

The sizing problems deal with the determination of

the size of a system in order to transfer heat at a

specified rate for a specified temperature difference.

Fourier's law of conduction

Qcond=- Λ A*dT/dx (W)

The thermal conductivity Λ of a material is the rate of heat transfer through a unit thickness of

the material per unit area and per unit temperature

difference.

10. Convection

Q_conv=hA_s(T_s-t_∞)

h - convection heat transfer coefficient; unit: W/(m2K)

AS - surface area through which convection heat transfer

takes place

TS - surface temperature

T∞ - temperature of the fluid sufficiently far from

the surface.

11.RADIATION

Q_rad=εσA_s(T_s⁴-T_surr⁴)

where:

- emissivity of the surface; 0 ≤ ε ≤ 1

AS - surface area

Ts- surface temperature

Tsurr- average surrounding surface temperature

σ = 5.67x10­^-8 (W / m²K⁴)

Stefan-Boltzmann constant

12. 1D Fourier`s law of heat conduction

Qcond=- Λ A*dT/dx (W)

13. Thermal resistance

Convection heat transfer -

from a solid surface of area AS and temperature TS to a

fluid sufficiently far from the surface of temperature T∞ and a

convection heat transfer coefficient h.

Rconv=1/(hA_s) (⁰C/W)

Convection heat transfer -

from a solid surface of area AS and temperature TS to a

fluid sufficiently far from the surface of temperature T∞ and a

convection heat transfer coefficient h.

Rrad=1/(h_radA_s) (⁰C/W)

Convection and radiation → total heat transfer

hcombined = hconvection + hradiation

Thermal resistance network

1D heat flow through a plane wall of thickness L, area A,

and thermal conductivity Λ , exposed to convection on

both sides to fluids at temperatures T∞ 1 and T∞ 2with heat

transfer coefficients h1 and h2, respectively

14. LUMPED SYSTEM

T =f(t)

T (x,y,z)=const

h – heat transfer coefficient

Energy balance of the solid for the time interval dt: hA_s(T_∞-T)dt=mC_pdT

Lumped system – great convenience in heat transfer analysis

Criterion for the applicability

→ definition of a characteristic length: L_c=V/A_s

and a Biot number Bi=hL_c/ Λ

Fourier number: τ=αt/L^2

15. In fluid – convection and

conduction (in the absence

of bulk motion)

For the temperature at the contact point of two bodies –

no-temperature-jump condition

qconv=Qconv

Nusselt number Nu= hL_c/ Λ , dimensionless convection

heat transfer coefficient

16.

17. Laminar flow – highly ordered → smooth streamlines;

typical cases – high-viscosity fluids (i.e. oils) at low velocities.

Turbulent flow – highly disordered → fluctuations;

typical cases – low-viscosity fluids at high velocities.

18. Thermal radiation – energy transitions of molecules, atoms

and electrons of a substancje.

The electromagnetic wave spectrum 1µm=10^-6m.

19. A blackbody adsorbs all

incident radiation and emits

radiation energy uniformly in

all directions per unit area

normal to direction of

emission → diffuse emiter

Spectral blackbody emissive power Ebλ

– the amount of radiation

energy emitted by a blackbody

at an absolute T per unit time,

per unit surface area, and per

unit wavelength about the

wavelength λ.

20. ABSORPTION and EMISSION

Assumption: A small body of surface area AS, emissivity ε,

and absorptivity α at temperature T contained in a large

isothermal enclosure.

ε (T) =α (T)

The total emissivity of a surface

at temperature T is equal to its

total absorptivity for radiation

coming from a blackbody at the

same temperature.

Radiation heat transfer

between a room and its

window is proportional to the

emissivity of the glass

surface.

21. The greenhouse effect

The spectral transmittivity of low-iron glass at room T for

different thickness

Glass transmits over 90% of radiation in the visible range and

is nontransparent to radiation in the IR range (λ > 3 m).

22. Boiling and evaporation - the liquid-to-vapour

phase change processes that occur at a solidliquid

interface when the surface is heated

above the saturation temperature Tsat of the

liquid → convection heat transfer.

Evaporation occurs when the vapour

pressure is less than the saturation

pressure of the liquid at a given

temperature, and it involves no

bubble formation or bubble motion.

Boiling occurs when a liquid is

brought into contact with a surface

maintained at a temperature TS

sufficiently above the saturation

temperature Tsat of the liquid.

Condensation

Temperature of a vapour - reduced below Tsat

23. Mass transfer requires

the presence of two

regions at different

chemical compositions

→ movement of

chemical species from a

high concentration

region toward a lower

concentration (nonhomogeneous

medium).

Mass diffusion

Concentration difference is the driving force for mass transfer.

Mass flow rate ∝ Normal area A ⋅ Concentration gradient dC/dx

Moisture – influence on the performance and durability of

building materials → importance of moisture transmission

Moisture – affects the

effective thermal

conductivity of porous

building materials →

linear increase of heat

transfer

Diffusion in a moving medium

Mass transfer - due to both diffusion and convection

24. Waves transfer energy (kinetic and potential energy of

medium particles).

Energy transfer – through matter due to displacement of

disturbance not involving translational motion of matter.

25. Wave superposition rule

If disturbances are produced by two wave motions, the

resultant (total) wave is the algebraic sum of the waves

acting on their own.

Note: The covering waves do not influence each other.

Wave interference

Let`s consider two waves with the same frequencies and

amplitudes but with a phase difference of ϕ : y1 = A sin (kx – ωt – ϕ) y2 = A sin (kx – ωt)

The total wave equation – from the superposition rule:

yw = y1 + y2 = A sin (kx – ωt – ϕ) + A sin (kx – ωt)

25. Sound wave intensity

Wave intensity I at a point is defined as the average velocity of

incoming energy to (or passing through) a unit surface (power)

Doppler effect

Christian Doppler (1842 r) found that when the source and

receiver of waves are in relative motion, the wave frequency,

as measured by the receiver, is different from the source

frequency.

Sound waves

The case of motion of the source and receiver along the

connecting straight line.