thermadynamics

JEE Mains 2015 Online › Thermal physics questions › thermadynamics

find the ratio of adiabatic bulk modulus and isothermal bulk modulus of a gas ? Î³=C_P/C_V

#Physics #Thermal physics

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5 Answers

106

Asish Mahapatra ·2009-03-21 04:28:54

ans is Î³ = Cp/Cv reason coming up

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3

iitimcomin ·2009-03-21 04:31:20

B = P.V/dV

i think its simple further...........

remember laplace correction derivation......................

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106

Asish Mahapatra ·2009-03-21 04:35:17

Bulk Modulus = volume stress / volume strain
= -V.Î”P/Î”V

If u consider isothermal expansion. then PV=const
differentiating
==> PÎ”V + VÎ”P = 0
==> B = -(V.Î”P/Î”V) = P

For adiabatic expansion.
PV^Î³ = const
taing log.
logP + Î³logV = const
differentiating
Î”P/P + Î³Î”V/V = 0
==> B = -(V.Î”P/Î”V) = -Î”P/(Î”V/V) = Î³P

so the ration is Î³

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106

Asish Mahapatra ·2009-03-21 04:39:33

i never derive this cuz i know that velocity of sound = √B/Ï

and Newton took isothermal so he got √P/Ï
while Laplace took adiabatic so got √Î³P/Ï

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Shriya ·2009-03-21 04:41:56

thank you

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