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