A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3)

Question

A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3) (A) 32 (B) 40/3 (C) 24/5 (D) 8

Tardigrade Admin · Accepted Answer

In an adiabatic process, P V&gamma; constant ⇒ (P1/P2)=((V2/V1))&gamma; ⇒ (P1/P2)=((1/8))5 / 3 ⇒ (P1/P2)=((1/23))5 / 3 =(1/32) (P2/P1)=32

Q. A monoatomic gas is suddenly compressed to $(1/8)^{t h}$ of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be $5/3$ )

32

40/3

24/5

8

In an adiabatic process,
$P V^{γ}$ constant
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{V _{2}}{V _{1}})^{γ}$
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{1}{8})^{5/3}$
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{1}{2 ^{3}})^{5/3}$
$= \frac{1}{32}$
$\frac{P _{2}}{P _{1}} = 32$

Q. A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be 5/3)

32

40/3

24/5

8

In an adiabatic process, PVγ constant ⇒P2​P1​​=(V1​V2​​)γ ⇒P2​P1​​=(81​)5/3 ⇒P2​P1​​=(231​)5/3 =321​ P1​P2​​=32

Q. A monoatomic gas is suddenly compressed to $(1/8)^{t h}$ of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be $5/3$ )

In an adiabatic process,
$P V^{γ}$ constant
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{V _{2}}{V _{1}})^{γ}$
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{1}{8})^{5/3}$
$\Rightarrow \frac{P _{1}}{P _{2}} = (\frac{1}{2 ^{3}})^{5/3}$
$= \frac{1}{32}$
$\frac{P _{2}}{P _{1}} = 32$