Instructor: Jaroslav Trnka
Physics 9B
Fall 2021
Formula sheet
Thermal expansion
Linear:
L = ↵L0 T . Volume:
V = V0 T ,
= 3↵
Heat and heat capacity
Specific: Q = mc T . Molar: Q = nC T . Fusion: Q = Lf m. Vaporization: Q = Lv m.
Heat transfer
Conduction: H =
Q
kA(T2 T1 )
=
. Radiation: H =
t
L
Q
= Ae (T24
t
T14 ).
Ideal gas
Gas equation: pV = nRT = N kB T . Change of internal energy:
Fixed mass of gas:
pV
T
U = nCV
T.
= const.
Molecules
Kinetic energy: K =
3
2 kT .
Speed: v =
q
3kT
m .
Molar heat capacities
Mass: m = nM , Capacities: CP = CV + R, Ratio of heat capacities:
=
CP
.
CV
General: CV = 12 R⇥(# degrees of freedom). Monoatomic: CV = 32 R. Diatomic: CV = 52 R.
Thermodynamic process
First law:
U =Q
W . Work: WA!B =
ˆ
B
p dV , cyclic process - thermal efficiency: e =
A
W
<1
QH
Special processes
Definition
Ideal gas
Work
Heat
Internal energy
Isochoric
V =0
pV = nRT
W =0
Q = nCV T
U =Q
Isobaric
P =0
pV = nRT
W = p(V2 V1 )
Q = nCP T
U =Q W
Isothermal
T =0
pV = nRT
W = nRT ln VV21
Q=W
U =0
Adiabatic
Q=0
pV = nRT, pV = const
W = nCV (T1 T2 )
Q=0
U= W
Constants
Gas: R = 8.31 J/K.mol, Boltzmann: k = 1.38 ⇥ 10 23 J/K, Avogadro: NA = 6.02 ⇥ 1023 /mol.
Stefan-Boltzmann: = 5.67 ⇥ 10 8 W/m2 .K4 .
Units
0 C = 273K,
1 mm = 10
3 m,
-3-
1 cm = 10
2 m,
1 dm = 10
1 m.