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 transformation, we have:

`PV^(\gamma)=const.`

where

P is the gas pressure

V is the volume

`\gamma` is the adiabatic index, which is
`\gamma=(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

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

where we know that

`(V_1)/(V_2)=(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:

`(P_2)/(P_1)=((1)/(4))^{(5)/(3)}=0.099`