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

Answer:

e) 0.099

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 $\frac{5}{3}$ 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:

$\frac{P_2}{P_1}=(\frac{V_1}{V_2})^{\gamma}=(\frac{V_1}{4V_1})^{5/3}=(\frac{1}{4})^{5/3}=0.099$