A polyatomic gas (γ=(4/3)) is compressed to (1/8) of its volume adiabatically. If its initial pressure is P0, its new pressure will be

Question

A polyatomic gas (&gamma;=(4/3)) is compressed to (1/8) of its volume adiabatically. If its initial pressure is P0, its new pressure will be (A) 8 P0 (B) 16 P0 (C) 6 P0 (D) 2 P0

Tardigrade Admin · Accepted Answer

For an adiabatic process, P V&gamma;= constant ∴ P((V0/8))4 / 3=P0(V0)4 / 3 or P=P0(8)4 / 3=P0(2)4=16 P0

Q. A polyatomic gas $(γ = \frac{4}{3})$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_{0}$ , its new pressure will be

$8 P_{0}$

$16 P_{0}$

$6 P_{0}$

$2 P_{0}$

For an adiabatic process,
$P V^{γ} =$ constant
$∴ P (\frac{V _{0}}{8})^{4/3} = P_{0} (V_{0})^{4/3}$
or $P = P_{0} (8)^{4/3} = P_{0} (2)^{4} = 16 P_{0}$

Q. A polyatomic gas (γ=34​) is compressed to 81​ of its volume adiabatically. If its initial pressure is P0​, its new pressure will be

8P0​

16P0​

6P0​

2P0​