A monatomic ideal gas in a container of fixed volume contains 4.10 × 10^24 atoms.
a) If you add enough thermal energy to double the root-mean-square speed of the gas atoms, by how much have you changed the entropy of the gas?
given monoatomic gas
ideal gas in a container
fixed volume, V
n = 4.1*10^24 atoms
a. rms speed is given by
Vrms = sqrt(3RT/Mm)
Mm is molar mass of the gas
so enough energy is added to double the RMS speed
hence, temperature increases by 4 times
hence internal energy increases 4 times
let initial internal energy be U
then final internal energy = 4U
also, for a constant volume process
dS = integral(dU/T) = integral(n*CvdT/T*Ao)
where Ao is avogadro's number
dS = n*Cv*ln(Tf/Ti)/Ao
Tf/Ti = 4
Cv = 3R/2 ( monoatomic gas)
dS = 107.022134088 J/K
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