A gas for which γ =1.5 is suddenly compressed to the (1/4) th of the initial volume. Then the ratio of the final to the initial pressure is

Question

A gas for which &gamma; =1.5 is suddenly compressed to the (1/4) th of the initial volume. Then the ratio of the final to the initial pressure is (A) 1:6 (B) 1:8 (C) 1:4 (D) 8:1

Tardigrade Admin · Accepted Answer

Here, &gamma; =1.5, V2=(1/4)V1; (p2/p1)=? As compression is sudden/adiabatic, ∴ p2V2&gamma; =p1V1&gamma; (p2/p1)=((V1/V2))&gamma; =(4)1.5=8

Q. A gas for which $γ = 1.5$ is suddenly compressed to the $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is

$1 : 6$

$1 : 8$

$1 : 4$

$8 : 1$

Here, $γ = 1.5, V_{2} = \frac{1}{4} V_{1}; \frac{p _{2}}{p _{1}} = ?$
As compression is sudden/adiabatic,
$∴ p_{2} V_{2}^{γ} = p_{1} V_{1}^{γ}$
$\frac{p _{2}}{p _{1}} = (\frac{V _{1}}{V _{2}})^{γ} = (4)^{1.5} = 8$

Q. A gas for which γ=1.5 is suddenly compressed to the 41​ th of the initial volume. Then the ratio of the final to the initial pressure is

1:6

1:8

1:4

8:1