During adiabatic process pressure P versus density ρ equation is:

Question

During adiabatic process pressure P versus density ρ equation is: (A) P ρ&gamma;= constant (B) P ρ-&gamma;= constant (C) P&gamma; ρ1+&gamma;= constant (D) P1 / &gamma; ρ&gamma;= constant

Tardigrade Admin · Accepted Answer

In adiabatic process, P V&gamma;= constant (1) Density ρ=(m/V) or ρ ∞ V-1 Hence, equation (1) can be written as p ρ-&gamma;= constant

Q. During adiabatic process pressure $P$ versus density $ρ$ equation is:

$P ρ^{γ} =$ constant

$P ρ^{- γ} =$ constant

$P^{γ} ρ^{1 + γ} =$ constant

$P^{1/ γ} ρ^{γ} =$ constant

In adiabatic process, $P V^{γ} =$ constant (1)
Density $ρ = \frac{m}{V}$
or $ρ \infty V^{- 1}$
Hence, equation (1) can be written as
$p ρ^{- γ} =$ constant

Q. During adiabatic process pressure P versus density ρ equation is:

Pργ= constant

Pρ−γ= constant

Pγρ1+γ= constant

P1/γργ= constant