Answer:
e) 0.099
Explanation:
For an adiabatic transformation, we have:
[tex]PV^{\gamma}=const.[/tex]
where
P is the gas pressure
V is the volume
[tex]\gamma[/tex] is the adiabatic index, which is [tex]\gamma=\frac{5}{3}[/tex] for an ideal monoatomic gas
The previous law can also be rewritten as
[tex]P_1 V_1 ^{\gamma}= P_2 V_2^{\gamma}[/tex]
or
[tex]\frac{P_2}{P_1}=(\frac{V_1}{V_2})^{\gamma}[/tex]
where we know that
[tex]\frac{V_1}{V_2}=\frac{1}{4}[/tex]
because the volume has increased by a factor 4.0. Substituting into the equation, we find by which factor the pressure has changed:
[tex]\frac{P_2}{P_1}=(\frac{1}{4})^{\frac{5}{3}}=0.099[/tex]
