# The isothermal bulk modulus of a perfect gas at atmospheric pressure is-

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The isothermal bulk modulus of a perfect gas at atmospheric pressure is-
1. 1.013 × 105 N/m2
2. 1.013 × 106 N/m2
3. 1.013 × 1010 N/m2
4. 1.013 × 1011 N/m2

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Correct Answer - Option 1 : 1.013 × 105 N/m2

Concept:

Compressibility is the reciprocal of the bulk modulus of elasticity.

Compressibility (p) = 1/K, and K = bulk modulus of Elasticity

${\rm{K}} = \frac{{{\rm{Increase\;of\;pressure}}}}{{{\rm{Volumetric\;strain}}}} = \frac{{{\rm{dP}}}}{{\frac{{ - {\rm{dv}}}}{{\rm{v}}}}} = \frac{{ - {\rm{dP}}}}{{{\rm{dv}}}} \times {\rm{V}}$      ----(i)

For isothermal process:

$\frac{{\rm{P}}}{{\rm{\rho }}} = {\rm{Constant}} \Rightarrow {\rm{P}} \times {\rm{V}} = {\rm{constant}}$      ----(ii)

Differentiating equation (ii),

PdV + Vdp = 0

⇒ PdV = -Vdp

$\Rightarrow {\rm{P}} = \frac{{ - {\rm{VdP}}}}{{{\rm{dV}}}}$      ----(iii)

From equation (i) & (iii), we have

K = P

The magnitude of atmospheric pressure is 1.013 × 105 N/m2

For adiabatic condition, $\frac{{\rm{P}}}{{{{\rm{\rho }}^{\rm{k}}}}} =$ constant, where γ = Ratio of specific heats.

Bulk modulus, K = γP