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

e) 0.099

Explanation:

For an adiabatic expansion:

where

P1 is the initial pressure

P2 is the final pressure

V1 is the initial volume

V2 is the final volume

is the adiabatic index (which is for an ideal monoatomic gas

In this problem, we have

since the volume increases by a factor 4

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

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