For an isothermal expansion of a perfect gas, the value of (Δ P/P) is equal of

Question

For an isothermal expansion of a perfect gas, the value of (Δ P/P) is equal of (A) - &gamma;1 backslash2 (Δ V/V) (B) - (Δ V/V) (C) - &gamma;(Δ V/V) (D) - &gamma;2(Δ V/V)

Tardigrade Admin · Accepted Answer

Differentiate PV = constant w.r.t V ⇒ P Δ V+V Δ P=0 ⇒ (Δ P/P)=-(Δ V/V)

Q. For an isothermal expansion of a perfect gas, the value of $\frac{Δ P}{P}$ is equal of

$- γ^{1\2} \frac{Δ V}{V}$

$- \frac{Δ V}{V}$

$- γ \frac{Δ V}{V}$

$- γ^{2} \frac{Δ V}{V}$

Differentiate $P V =$ constant w.r.t $V$
$\Rightarrow P Δ V + V Δ P = 0$
$\Rightarrow \frac{Δ P}{P} = - \frac{Δ V}{V}$

Q. For an isothermal expansion of a perfect gas, the value of PΔP​ is equal of

−γ1\2VΔV​

−VΔV​

−γVΔV​

−γ2VΔV​