Question

If an ideal monatomic gas undergoes an adiabatic expansion, in which the volume increases by a factor of 4.0, by what factor does the pressure change?

a) 2.1
b) 1.7
c) 0.52
d) 0.25
e) 0.099

Answer 1

e) 0.099

Step-by-step explanation:

For an adiabatic expansion:

`P_1 V_1^(\gamma) = P_2 V_2^(\gamma)`

where

P1 is the initial pressure

P2 is the final pressure

V1 is the initial volume

V2 is the final volume

`\gamma` is the adiabatic index (which is
`(5)/(3)` for an ideal monoatomic gas

In this problem, we have

`V_2 = 4 V_1` since the volume increases by a factor 4

We can re-write the equation to find by what factor the pressure changes:

`(P_2)/(P_1)=((V_1)/(V_2))^(\gamma)=((V_1)/(4V_1))^(5/3)=((1)/(4))^(5/3)=0.099`