Question

If in an adiabatic process, the pressure is increased by 2/3%, then the volume decreases by ______.

`("Assume", "C"_"p"/"C"_"v"=3/2)`

Options

• `4/9`%

• `2/3`%

• 4%

• `9/4`%

Answer 1

If in an adiabatic process, the pressure is increased by 2/3%, then the volume decrease by `underlinebb(4/9%)`.

Explanation:

PV^γ = constant

γ = `"C"_"p"/"C"_"v"=3/2`

pV^3/2 = constant

⇒ log P + `3/2` log V = log C

⇒ `(Delta"P")/"P"+3/2(Delta"V")/"V"` = O

⇒ `(Delta"V")/"V"=-2/3(Delta"P")/"P" `

∴ `(Delta"V")/"V"xx100=(2/3)((Delta"P")/"P"xx100)`

= `(2/3xx2/3)`%

= `4/9`%