Question

In an adiabatic process, the pressure is increased by 2/3 %. If γ = 3/2, then the volume decreases by nearly(a) 4/9 %(b) 2/3 %(c) 1%(d) 9/4 %

Answer 1

Answer: (A). The volume decreases 4/9%

Explanation:

Given that,

Increased pressure $\dfrac{\Delta p}{p} = \dfrac{2}{3}$

$\gamma= \dfrac{c_{p}}{c_{v}}=\dfrc{3}{2}$

We know that,

$PV^{\gamma}= c$....(I)

Where,

$\gamma = \dfrac{c_{p}}{c_{v}}$

Put the value of $\gamma$ in equation (I)

$P V^{\dfrac{c_{p}}{c_{v}}} = c$

Taking log both sides

$log P+\dfrac{3}{2}\ logV= log c$

On differentiate..

$\dfrac{\Delta P}{P}+\dfrac{3}{2}\dfrac{\Delta V}{V}= 0$

$\dfrac{\Delta V}{V}= -\dfrac{2}{3}\dfrac{\Delta P}{P}$

Negative sign represent of decrements of volume

$\dfrac{\Delta V}{V}\times 100= \dfrac{4}{9}\%$

Hence, The volume decreases 4/9%

Answer 2

Answer:- Option A

The volume decreases by nearly 4/9%