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 transformation, we have:

$PV^{\gamma}=const.$

where

P is the gas pressure

V is the volume

$\gamma$ is the adiabatic index, which is $\gamma=\frac{5}{3}$ for an ideal monoatomic gas

The previous law can also be rewritten as

$P_1 V_1 ^{\gamma}= P_2 V_2^{\gamma}$

or

$\frac{P_2}{P_1}=(\frac{V_1}{V_2})^{\gamma}$

where we know that

$\frac{V_1}{V_2}=\frac{1}{4}$

because the volume has increased by a factor 4.0. Substituting into the equation, we find by which factor the pressure has changed:

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