Post on 22-Dec-2021
โข thermodynamic work
โข 1st law of Thermodynamics
โข equation of state of the ideal gas
โข Isochoric, isobaric, and isothermal process in ideal gas
Lecture 29: 1st Law of Thermodynamics
Thermodynamic work
๐ = เถฑ๐
๐
๐ ๐, ๐ ๐๐
work done by the gas
Work and p-V curve
๐ = เถฑ๐
๐
๐ ๐, ๐ ๐๐
๐ > 0 if gas expands (ฮ๐ > 0)
๐ < 0 if gas is compressed (ฮ๐ < 0)
work done by the gas
โน area under the ๐ โ ๐-curve
First Law of Thermodynamics
The internal energy of a system can change:
โข Heat flow in or out of system
โข Work done on or by gas
ฮ๐ = ๐ โ ๐
๐: net heat flowing into the system
๐: work done by the system
ฮ๐ is completely determined by initial and final
values of the state variables
(even though ๐ and ๐ depend on the process!)
Internal energy
Internal energy ๐ of the system
= kinetic energies of particles
+ potential energy of interaction
Value of ๐ depends on state of system only.
State is characterized by state variables such as:
temperature, pressure, volume, phase
Ideal gas
โข particles do not interact with each other
โข only elastic collisions between particles and with walls
Real gas can be treated as ideal if:
low density, low pressure, high temperature
State variables are related by:
๐๐ = ๐๐ ๐
๐ number of moles
๐ universal gas constant
๐ =8.315J/(molโ K)
No interactions between particles
โน ๐ consists only of kinetic energies of particles
โน ๐ depends only on temperature: ๐ = ๐(๐) * * Only true
for ideal gas!
Important processes for the ideal gas
V
P P P
V Vp=const.isobaric
V=const.isochoric
T=const.isothermal
Adiabatic Process
P
V
๐ = 0๐๐ ๐พ = ๐๐๐๐ ๐ก๐พ = ๐๐/๐๐
๐พ = 1.67 ๐๐๐๐๐๐ก๐๐๐๐๐๐ 1.40 (๐๐๐๐ก๐๐๐๐)
๐พ > 1 steeper than isothermal
Isochoric process for the ideal gas
Isobaric process for the ideal gas
Isothermal process for the ideal gas
Isobaric vs isochoric process
Consider two process between same two temperatures:
Isochoric: ฮ๐ = ๐๐๐ฮ๐
Isobaric: ฮ๐ = ๐๐๐ฮ๐ โ ๐ฮ๐
๐๐๐ฮ๐ = ๐๐๐ฮ๐ โ ๐ฮ๐
with ๐ฮ๐ = ๐๐ ฮ๐:
๐๐ โ ๐๐ = ๐
To increase U by same amount as in isochoric process,
more Q needed for isobaric process because gas is doing work
V
Difference between ๐๐ and ๐๐
Monoatomic gas: ๐๐ =3
2๐ , ๐๐ =
5
2๐
Diatomic gas: ๐๐ =5
2๐ , ๐๐ =
7
2๐
๐๐ โ ๐๐ = ๐
Mono- vs diatomic gas
Monoatomic gas: ๐๐ =3
2๐ , ๐๐ =
5
2๐
Diatomic gas: ๐๐ =5
2๐ , ๐๐ =
7
2๐
Each degree of freedom in the kinetic energy
contributes 1
2๐ to specific heat
Monoatomic gas: 3 directions for translation
Diatomic gas: 3 translations, 3 rotations,
but very small moment of inertia about one axis,
this rotation does not contribute
Adiabatic Process
P
V
๐ = 0 โ ฮ๐ = โ๐