SPECIFIC HEAT AT CONSTANT VOLUME AND PRESSURE
(1) Whensolids and liquids are heated at constant pressure, the changes in volume are so small that they are negligible as compared to their initial volumes. The external work done (= pdV) is negligible. Hence wedo not consider two specific heats for solids and liquids.
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(2) The difference between the principal specific heats cp - cy is given by Mayer's relation, viz. c - c = r where r is the gas constant for unit mass.
p V c
If Cp and Cv denote the molar specific heats, then Cp - Cv = R, where R is the universal gas constant and all the quantities are expressed in SI units.
r - 77 . The value of R is the same for all gases but the value of r is different M
for different gases. •
(3) If cp and'cv are expressed in heat units and r in mechanical units, then
cp - cy = t where J is the mechanical equivalent of heat.
Similarly Cp - Cy = y . CP
(4) The ratio is called the adiabatic constant (y).
(5) Dimensional Equations of quantities used in heat:
Sofar we have considered the dimensions of.physical quantities used in mechanics. While finding the dimensions of physical quantities used in heat, we consider the temperature (0) as a fundamental quantity, in addition to L, M and T. However, the unit for temperature is Kelvin (K).
The dimensional equations for various quantities in heat are givenbelow :
(1) [Temperature] = [M° L° T° 01]
(2) Heat is a form of energy. Hence it has the dimensions of work. The dimensional equation of heat energy is [H] = [M1 L2 T~2]
Quantity of heat (AQ)
(3) Specific heat (S) - mass x difference in temperature (A0)
v. [S] = ^T1 =-[M°L2T-29~1] [M'e1]
(4) Molar specific heat = —— where n is the number of moles of the gas
[M1 L2 T~2]
[Molar specific heat] = —--—r~ = [M1 L2 T~2 6-1 mol"1]
(5) Universal gas constant (R).
v PV = nRT R = -
\ nT •
[R]= [M'L-IT-^L3] =[M.L2T-29-.mor,] '
[mol x 86]
(6) Wien's constant b = AmT
.-. [b] = [L101] = [M°L1Toe1]
E _ Energy per unit area per unit time
(7) Stefan's constant o = - --
[CT] = = [M' l0^3 9~4]
[L7 T1 04]
(8) Emissive power E = —-
A x t
[E] = ^L2T-2] = [Mi L0T-3 90] [L2 T1 ]
(9) Latent heat: vQ = mxL V '
M-rQI-^W = [M°L2T-2] LmJ [M1]
(10) Boltzmann Constant (K):
From kinetic theory of gases, E = — KT
.•. K = — — , p.], = [M1 L2 T'2 9~']
3 T [8 ]