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10 Heat and Matter
where k is Boltzmann constant, T the absolute temperature, m the particle mass,
R the gas constant and M the molecular weight.
λ =
v
4π
√
2 r 2 N
(10.8)
where N = nV , n is the number of molecules per unit volume and V is the volume
of the gas.
Gas Laws
PV = n RT
(gas equation)
(10.9)
ρ 1 T 1
P 1
=
ρ 2 T 2
P 2
(10.10)
Thermal Expansion
L = L 0 [1 + ααT ]
(linear expansion)
(10.11)
β = 2α, γ = 3α
(10.12)
where α is the coefficient of linear expansion, β is the coefficient of areal expansion
and γ that of volume expansion.
Thermal Expansion and Elasticity
Force F = Y aααT
(10.13)
where Y is Young’s modulus and a the cross-sectional area.
The coefficient A of apparent expansion of a liquid
A = γ − g = γ − 3α
(10.14)
where γ is the absolute volume coefficient of expansion of liquid and g that of the
container.
Apparent expansion of liquid =
mass expelled
(mass left)(temperature rise)
Heat Transfer
Heat conduction through a slab:
−
dQ
dr
= k 1 A
T 1 − T 2
d
(10.15)
10 Heat and Matter
where k is Boltzmann constant, T the absolute temperature, m the particle mass,
R the gas constant and M the molecular weight.
λ =
v
4π
√
2 r 2 N
(10.8)
where N = nV , n is the number of molecules per unit volume and V is the volume
of the gas.
Gas Laws
PV = n RT
(gas equation)
(10.9)
ρ 1 T 1
P 1
=
ρ 2 T 2
P 2
(10.10)
Thermal Expansion
L = L 0 [1 + ααT ]
(linear expansion)
(10.11)
β = 2α, γ = 3α
(10.12)
where α is the coefficient of linear expansion, β is the coefficient of areal expansion
and γ that of volume expansion.
Thermal Expansion and Elasticity
Force F = Y aααT
(10.13)
where Y is Young’s modulus and a the cross-sectional area.
The coefficient A of apparent expansion of a liquid
A = γ − g = γ − 3α
(10.14)
where γ is the absolute volume coefficient of expansion of liquid and g that of the
container.
Apparent expansion of liquid =
mass expelled
(mass left)(temperature rise)
Heat Transfer
Heat conduction through a slab:
−
dQ
dr
= k 1 A
T 1 − T 2
d
(10.15)