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

 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. µ 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 µ e) f) C = C0 C0 = R.M.S. speed at 0°C, C = R.M.S. speed at t°C, 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 µ 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

Þ

 m M

=1

(For n = 1)

\ m = M

Mass of the gas = Molecular weight

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