If no heat is wasted to the surroundings then heat gained = heat lost when two bodies are in contact.
Thermal capacity or water equivalent W = mc
Specific heat of gases is of two type’s specific heat of gases at constant volume (Sv) and specific heat of gases at constant pressure (sp).
Sv= [ΔQ / m Δ T] constant volume
And molar specific heat at constant volume
Cv = ( Δ Q / n Δ T) constant volume
sp = [ Δ Q / m Δ T] constant pressure
And molar specific heat at constant pressure is
Cp = ( Δ Q / n Δ T) constant pressure
Mayer formula Cp – Cv = R
Note that Cv (adiabatic process) = 0
Cv (isothermal process) = ∞
Law of equipartition of energy each degree of freedom in a gas average contributes equal energy (average) 1 / 2 KT/
Molecule or 1 / 2 RT per mole.
For a monatomic gas
Cv = 3 / 2 R; Cp = 5 / 2 R and γ = Cp / Cv = 5 / 3 = 1.67
Number of degrees of freedom = 3 (all translational.).
For the a diatomic gas
Cv = 5 /2R, Cp = (7/2)R γ= 7/5 = 1.4
Number of degrees of freedom = 5 (3 translation + 2 rotation) assuming molecules if not vibrate.
There are certain gases which do vibrate. In such cases, number of degrees of freedom = 7.
Cv = ( 7 / 2) R, Cp = (9 / 2) R (Cp / Cv ) = (9 / 2) = 1.29
For polyatomic gases number of degrees of freedom = 6 (3 translation, 2 rotation and 1 vibration)
Cv = 3R, Cp = 4R γ = Cp / Cv = 4 / 3
If all the degrees of freedom (translational rotational and vibration) are excitable then for an N – atomic molecule (volume or network). Number of degrees of freedom = (6N – 3). For an N – atomic linear molecule number of degrees of freedom = (6N – 5)
Delong petite’s law specific heat of solids at constant volume = 3R or 6 calmol-10C-1. It is valid at high temperature. It is based on the fact that there are 3 N vibration states for N molecules.
For a mixture of gases
γmix = Cpmix / Cvmix
Cvmix = n1 Cv1 + n2 Cv 2 / n1 + n2 Cpmix = Cv mix + R
Specific heat of H2 is max. [3.5 cal g -1°C-1]. This is followed by water [1 calg -1°C-1] it is minimum for radon and actinium [0.22 calg -1 – 0°C-1].
At low temperature, specific heat C ∝ T8 (in super-conducting range) and at high temperature C ∝ T.
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