# Specific Volume

SPECIFIC HEAT AT CONSTANT VOLUME AND PRESSURE

Note :

(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

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

r

cp - cy = t where J is the mechanical equivalent of heat.

i

R

Similarly Cp - Cy = y . CP

(4) The ratio is called the adiabatic constant (y).

cv

(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]

AQ

(4) Molar specific heat = —— where n is the number of moles of the gas

n AG

[M1 L2 T~2]

[Molar specific heat] = —--—r~ = [M1 L2 T~2 6-1 mol"1]

[mol [0]]

(5) Universal gas constant (R).

PV

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

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(7) Stefan's constant o = - --

[CT] = = [M' l0^3 9~4]

[L7 T1 04]

Q •

(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):

3

From kinetic theory of gases, E = — KT

.•. K = — — , p.], = [M1 L2 T'2 9~']

3 T [8 ]