Lecture 5 - Farmaceutická fakulta Univerzity Komenského ... · J E 4 6 8 Each gas exerts the same...

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Lecture 5 Physics 2017/2018

Transcript of Lecture 5 - Farmaceutická fakulta Univerzity Komenského ... · J E 4 6 8 Each gas exerts the same...

Lecture 5

Physics 2017/2018

Temperature – T (t) –

Intrinsic property –

independent on the

amount of the material

temperarure = average kinetic

energy of molecules

[T] = 1 K = 1oC

T = t + 273.15 oC

Thermal physics

Measurement of temperature

properties of materials varying with temperature

• volume

• electrical properties

• pressure (gauges thermometers)

• IR radiation….

• Temperature scalesKelvin – [T] = 1 KCelsius – [t] = 1 oC

0 oC = 273.15 K100 oC = 373.15 Kwater freezing-boiling

T1 K = (t1 + 273.15 ) oCT2 K = (t2 + 273.15 ) oC(T1 - T2) K = (t2 - t2 ) oC

T=0K => p=0, V=0 impossibleto reach

• Thermal expansion of materials

α – linear (area, volume ) thermal expanson coefficient [α]=K-1

• Density variation with temperature

Density decreases with increasing temperature!

• Anomaly of water density

0<t<3.98oC β<0, the density increases with t

t=3.98oC β=0, density has maximum

t> 3.98oC β>0, density decreases with t “normal” behaviour

• Thermodynamics – branch of physics concerned with heat and temperature and their relation to energy and work

Thermodynamic system is the content of a macroscopic volume in space, along with its walls and surroundings; it undergoes thermodynamic processes according to the principles of thermodynamics.

Thermodynamic systems –

• open system – energy, matter exchange

• closed system – energy, matter exchange

• isolated system - energy, matter exchange

State functions - their values do not depend on the path, done by the system to get to the given state (internal energy, entropy...)

Process (path) functions – heat, work depend on the path

intensive – independent on the number particles, T, p, Vm…

extensive – dependent… V, n

but

Vm=V/n molar volume – intensive

Vs=V/m specific volume - intensive

ΔX12= -ΔX21

ΔXA= -ΔXB =- ΔXC ΔX= ΔX1 +ΔX2 +ΔX3 +ΔX4

State functions

Exact differential (total differential)

example

Ideal gas

• the molecules are point-like particles

• elastic collisions

• no interactions between the particles, except the collisions

Real gases behave similarly at high temperatures and low densities

• molecules have non-zero volume

• interactions

• not allways elastic collisions

• Brownian motion

• Thermodynamic state – system fully identified

with a suitable set of state variables (function) for examples: pressure p, volume V, temperature T, number of moles n.

Gay-Lussac I. law, Charles’ law, Law of Volumes isobaric processp = const.

Pressure – temperature law, Gay-Lussac II.lawisochoric processV= const.

Boyle-Mariotte law isothermal process

T=const.

pV= const.

Avogadro’s lawUnder the same conditions of temperatureand pressure, equal volumes of differentgases contain an equal number of molecules(regardless on their chemical nature andphysical properties).

NA= 6.02214129 × 1023

Vm=22,41 dm-3=22,41 l(T=273,15K,p= 101 325 Pa)

Avogadro’s number or Avogadro‘s constant.

𝑉 = 𝑛 𝑘

p=101 325 Pa, T= 273.15 K Vm = 22.41 L = 0.02241 m-3

NA=6.022x1023

Ideal gas lawGay-Lussac laws

V= const . T p= const . TBoyle-Mariotte

pV = constAvogadro

V = const . nIdeal gas law

pV=n R T

R= 8.314 JK-1mol-1 universal gas constantk= R/NA = 1.3806 x 10-23 JK-1 Boltzmann constantpV=N kBT kB–bridge from macroscopicN=nNA to microscopic physics

Dalton´s law – mixture of gases

𝑛 = 𝑛𝑖𝑖

𝑝 =𝑛𝑅𝑇

𝑉= 𝑛𝑖𝑖 𝑅𝑇

𝑉= 𝑝𝑖

𝑖

In a mixture of non-reacting gases, the total pressure exerted

is equal to the sum of the partial pressures of the individual

gases. 𝑝𝑖 =𝑛𝑖𝑅𝑇

𝑉

Each gas exerts the same pressure they would exert if they

were in the container alone.

Real gases

Real gases – particles not point mass, real volume

– not negligible interactions, attraction-repulsion,

non-elastic collisions.

van der Waals equation

𝑝 +𝑛2𝑎

𝑉2 𝑉 − 𝑛𝑏 = 𝑛𝑅𝑇

𝑛2𝑎

𝑉2 - correction for non-elastic interactions, attraction-

repulsion

𝑛𝑏 – correction for the real volume of particles

a,b – material constants, determined experimentaly

• Heat and temperature

Q [Q] = 1 J (energy)

transfer of heat – change

of temperatures

c – heat capacity [c] = J K-1

cm – molar heat capacity [cm] = J mol-1K-1

cs – specific heat capacity [cs] = J kg-1K-1

• Work of ideal gases (W, A) [W] = 1J

W = -Fex Δx = -p S Δx = -p ΔV

Sign convention – from the point of view of the systemreceives releases

Q: + -

W=-∫pdV + -ΔV<0 compression ΔV>0 expansion

Zeroth law of thermodynamics

If two bodies are each in thermal equilibriumwith some third body, then they are also in equilibrium with each other.

Thermodynamic equilibrium (steady) stateequilibrium – stable, unstable, indifferentThermodynamic equilibrium, condition or state of a

thermodynamic system, the properties of which do not change with time and that can be changed to another condition only at the expense of effects on other systems.

entropy (at given energy)- maximum,Gibbs free energy (at given p, T) - minimum

Reversible process – is a process that can be "reversed" by means of infinitesimal changes in some property of the system. A reversible process does not increase entropyof the system and surroundings. During a reversible process, the system is in thermodynamic equilibriumwith its surroundings throughout the entire process.

Real processes are not reversible!