10.1 Basic Concepts and Formulae
413
Heat Engines Thermodynamic efficiency
e =
Work done by the gas
Heat put into the system
=
W
Q in
(10.28)
The Carnot cycle consists of two isothermal processes and two adiabatic processes.
The Sterling cycle consists of two isothermal processes and two isochoric processes.
The Otto cycle consists of two adiabatic processes and two isochoric processes.
e = (Q H − Q C )/Q H
(10.29)
e = (T H − T C )T H
(10.30)
where the symbols H and C are for hot and cold reservoirs.
Elasticity
Stress = force/area = F/A
Strain = elongation/original length = L/L
Young’s modulus(Y ) = stress/strain = F L/AL
Shear modulus (η) = shear stress/shear strain = F y/Ax
Bulk modulus (K ) = pressure increment/volume strain =
P
−V /V
Poisson’s ratio (σ ) = lateral contraction per unit length/longitudinal elongation
per unit length.
Relations for the elastic moduli:
Y =
9ηK
3K + η
= 2n(1 + σ ) = 3K (1 − 2σ )
(10.31)
σ =
3K − 2η
6K + 2η
(10.32)
Surface Tension
Excess pressure in a drop
P = 2S/r
(10.33)
Excess pressure in a bubble
P = 4S/r
(10.34)
Pressure in a bubble due to electric charges
P = σ
2
/2ε 0
(10.35)
where σ is the charge density and ε 0 is the permittivity.