Answer:
e) 0.099
Explanation:
For an adiabatic expansion:
[tex]P_1 V_1^{\gamma} = P_2 V_2^{\gamma}[/tex]
where
P1 is the initial pressure
P2 is the final pressure
V1 is the initial volume
V2 is the final volume
[tex]\gamma[/tex] is the adiabatic index (which is [tex]\frac{5}{3}[/tex] for an ideal monoatomic gas
In this problem, we have
[tex]V_2 = 4 V_1[/tex] since the volume increases by a factor 4
We can re-write the equation to find by what factor the pressure changes:
[tex]\frac{P_2}{P_1}=(\frac{V_1}{V_2})^{\gamma}=(\frac{V_1}{4V_1})^{5/3}=(\frac{1}{4})^{5/3}=0.099[/tex]
