Thermodynamics Flashcards
Thermal linear expansion
ΔL = αLiΔT
Thermal volumetric expansion
ΔV = βViΔT
Relationship between volumetric expansion and linear expansion
β = 3*ɑ
for all isotropic solids
ideal gas law
PV = nRT
or
PV=NkBT
- n -> number of moles*
- N -> number of molecules*
- kB -> Boltzmann’s constant*
Energy and temperature change relationship
Q = mcΔT
Latent heat
Q = ± mL
energy required for a phase change
Work to expand or compress gas
W = -∫PdV
First law of thermodynamics
ΔEint = Q + W
internal energy is equal to heat transfered and work done on the system
Adiabatic process
No heat leaves or is added to a system
ΔEint = W
isobaric system
process occurs under constant pressure
W = -P(Vf - Vi)
Isovolumetric system
Process that takes place under constant volumn
ΔEint = Q
W = 0
work done during isothermal expansion
W = n*R*T*ln(Vi/Vf)
heat per second (power) transfered by coduction
P = kA|dT/dx|
|dT/dx| = (Th - Tc)/L
Pressure and molecular kinetic energy
P = 2/3*(N/V)*(1/2 m* vavg2)
Temperature and mean velocity
1/2 m*vavg2 = 3/2 kbT
vrms = sqrt(3RT/M) = sqrt(3kbT/m)
heat and temperature at constant volumn
Q = nCVΔT
heat and temperature at constant pressure
Q = nCPΔT
molar specific heat at constant volumn for ideal gas
CV = 3/2*R
ratio of specific heats in ideal gas
CP - CV = R
γ = CP/CV = 5/3
Constant during adiabatic process
PVγ = const
using ideal gas law:
TVγ-1 = const
Boltzmann distribution law
number of molecules at a certain energy
nV(E) = n0e-E/kbT
rms velocity
vrms = sqrt(3kT/m)
average velocity of gas molecules
vavg = sqrt(8kT/πm)
most probable speed of gas molecules
vmp = sqrt(2kT/m)
mean free path of gas molecule
l = 1/(√(2)πd2nV)
collision frequency of molecules
f = √(2)πd2vavgnV = vavg/l
effeciency of heat engine
e = Weng/|Qh| = 1 -|Qc|/|Qh|
Change in entropy (general)
dS = dQr/T
Qr -> amount of energy transfered by heat in a reversible process
Total change in entropy for carnot engine
0
change in entropy for ideal gas
ΔS = nCV*ln(Tf/Ti) + nR*ln(Vf/Vi)
entropy of macrostate
S = kbln(W)
W -> nuber of microstates of the system corresponding to mactrostate