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 c_{p} - c_{y} 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 C_{v} denote the molar specific heats, then C_{p} - C_{v} = 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 c_{p} and'c_{v} are expressed in heat units and r in mechanical units, then

r

c_{p} - c_{y} = t where J is the mechanical equivalent of heat.

i

R

Similarly C_{p} - C_{y} = y . ^{C}P

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

^{c}v

(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° 0^{1}]

(2) Heat is a form of energy. Hence it has the dimensions of work. The dimensional equation of heat energy is [H] = [M^{1} L^{2} T~^{2}]

Quantity of heat (AQ)

(3) Specific heat (S) - _{mass x} difference in temperature (A0)

v. [S] = ^T^{1} =-[M°L^{2}T-^{2}9~^{1}] [M'e^{1}]

AQ

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

n AG

[M^{1} L^{2} T~^{2}]

[Molar specific heat] = —--—r~ = [M^{1} L^{2} T~^{2} 6^{-1} mol"^{1}]

[mol [0]]

(5) Universal gas constant (R).

PV

v PV = nRT R = -

\ nT •

[R]= [M'L-IT-^L^{3}] _{=[M}._{L}2_{T}-2_{9}-._{mor},_{]} '

[mol x 8^{6}]

(6) Wien's constant b = AmT

.-. [b] = [L^{1}0^{1}] = [M°L^{1}T^{o}e^{1}]

E _ Energy per unit area per unit time

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(7) Stefan's constant o = - --

_{[CT] = =} [M' l^{0}^^{3} 9~^{4}]

[L^{7} T^{1} 0^{4}]

Q •

(8) Emissive power E = —-

A x t

[E] = ^L^{2}T-^{2}] _{= [M}i _{L}0_{T}-3 _{90] }[L^{2} T^{1} ]

(9) Latent heat: vQ = mxL ^{V} '

M-rQI-^W = [M°L^{2}T-^{2}] LmJ [M^{1}]

\

(10) Boltzmann Constant (K):

3

From kinetic theory of gases, E = — KT

.•. K = — — , p.], _{=} [M^{1} L^{2} T'^{2} 9~']

3 T [8 ]