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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Kinetic Theory of Gases Formulae Page 1

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1. Pressure Exerted by an Enclosed Gas

 

p

=

1

 

Nm0C2

=

1

 

mC2

=

1

rC2

 

 

 

 

 

3

V

3

V

3

 

m0

= mass of gas molecule

m

= mass of gas

C

= rms velocity of gas molecules

r

= Density of gas

N

= Total number. of gas molecules

 

2. K.E. Per Unit Volume of a Gas

 

K.E. per unit volume of a gas =  

3

P

 

2

 

3. K.E. Per Mole of a Gas

 

K.E. per mole of a gas =  

3

RT

=

1

MC2

 

 

2

2

M = molecular weight

 

4. K.E. Per Molecule of a Gas

 

K.E. per molecule of a gas =

3

 

RT

=

3

kT =

1

m0C2

 

 

 

 

2

N0

2

2

N0 = Avogadro's no.,

R

= k = Boltzmann constant

 

N0

 

5. K.E. Per Unit Mass of a Gas

 

K.E. per unit mass of a gas =

3

 

RT

=

1

C2

 

 

 

2

M

2

 

6. Relation Between K.E. And Temperature

 

K.E. of a gas molecule is proportional to its absolute temperature (K.E. T)

 

7. R.M.S. Velocity

a)

RMS velocity C = =

 

b)

C =

 

 

c)

C =

R: Universal Gas constant, M: Molecular weight of gas molecule

 

 

d)

C

e)

 

f)

C = C0

 

C0 = R.M.S. speed at 0C,
C = R.M.S. speed at tC,
P = pressure,
r = density of the gas ,
R = Gas constant,
M = Molecular weight of gas molecule.

 

8. Ideal Gas Equation

 

GAS (A) : P1V1 = n1RT1

P1V1 =

m1

RT1

 

M1

GAS (B) :P2V2 = n2RT2

P2V2 =

m2

RT2

 

M2

 

\

P1V1

=

m1

M2

 

T1

 

 

 

 

P2V2

m2

M1

T2

 

9. Relation Between Pressure and Number of Molecules of the Gas

 

P N

\

P1

=

N1

 

 

P2

N2

 

10. First Law of Thermodynamics

 

dQ = dU + dW (all are in same units)
dQ = total heat energy supplied
dU = increase in internal energy
dW = external work done

 

11. Mayer's Relation

 

Mayer's relation (in heat units)

 

C'p - C'v = R/J
(Molar sp. heats)

Cp - Cv =

r

=

R

 

 

J

MJ

(Principal sp. heats)

 

 

 

 

 

Cp - Cv =

P

 

r JT

(Principal sp. heats)

 

12. Change in Internal Energy

 

dU

= mCv dT

(joule)

 

 

=

mCv dT

 

J

(Cal or kcal)

 

Cv is principal sp. heat at constant volume

joule

 

kg K

 

13. External Work Done

 

 

 

 

 

 

 

 

 

dU

= n C'v dT

(joule)

 

 

= n

C'v dT

 

J

(cal or kcal)

 

C'v is molar sp. heat at constant volume

joule

 

k - mole K

 

Work done dW

= PdV (joule)

 

 

=

PdV

 

J

  (Cal or kcal)

 

14. Latent Heat

 

L = Li + Le
Li = Internal latent heat
Le = External latent heat

Le = 

PdV (joule)

PdV

J

 

15. Relation Between Molar Specific Heat and Principal Specific Heat

 

Molar specific heat = Molecular weight Principal specific heat

 

16. Relation Between Mass of the Gas And Molecular Weight

 

 

 

m

M

 =n

  

m

M

 =1

(For n = 1)

 

 

 

 

 

 

\ m = M

 

Mass of the gas = Molecular weight

 

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