The bulk modulus of a gas is defined as B = - Vdp / d V. For an adiabatic process the variation of B is proportional to pn . For an ideal gas n is

Question

The bulk modulus of a gas is defined as B = - Vdp / d V. For an adiabatic process the variation of B is proportional to pn . For an ideal gas n is (A) zero (B) 1 (C) 5/3 (D) 2

Tardigrade Admin · Accepted Answer

Adiabatic bulk modulus for an ideal gas is K=(dp/-dV/ V)=-V((dp/dV)) = &gamma; p ⋅s(i) Now given, K propto pn ⋅s(ii) ∴ From Eqs. (i) and (ii), we have ⇒ n=1

Q. The bulk modulus of a gas is defined as $B = - V d p / d V .$ For an adiabatic process the variation of $B$ is proportional to $p^{n}$ . For an ideal gas $n$ is

zero

1

5/3

2

Adiabatic bulk modulus for an ideal gas is
$K = \frac{d p}{- d V / V} = - V (\frac{d p}{d V})$
$= γ p \dots (i)$
Now given,
$K \propto p^{n} \dots (ii)$
$∴$ From Eqs. $(i)$ and $(ii),$ we have
$\Rightarrow n = 1$

Q. The bulk modulus of a gas is defined as B=−Vdp/dV. For an adiabatic process the variation of B is proportional to pn . For an ideal gas n is

zero

1

5/3

2

Adiabatic bulk modulus for an ideal gas is K=−dV/Vdp​=−V(dVdp​) =γp⋯(i) Now given, K∝pn⋯(ii) ∴ From Eqs. (i) and (ii), we have ⇒n=1

Q. The bulk modulus of a gas is defined as $B = - V d p / d V .$ For an adiabatic process the variation of $B$ is proportional to $p^{n}$ . For an ideal gas $n$ is

Adiabatic bulk modulus for an ideal gas is
$K = \frac{d p}{- d V / V} = - V (\frac{d p}{d V})$
$= γ p \dots (i)$
Now given,
$K \propto p^{n} \dots (ii)$
$∴$ From Eqs. $(i)$ and $(ii),$ we have
$\Rightarrow n = 1$