Given a 11 m3 tank which is occupied by 12 oC helium gas at atmospheric pressure

Question

Given a 11 m3 tank which is occupied by 12 oC helium gas at atmospheric pressure. Answer the following questions in SI units with 3 sig digits accuracy. Answers can be given in scientific notation, for example 4.29E-15 = 4.29 x 10-15

You may reference the periodic table for relevant data. Note that helium gas is monoatomic.

Other data (all in SI units) : Boltzmans constant = 1.38E-23 J/K , Avagadro's number = 6.022E23 mol-1 , Gas constant = 8.315 J/mol*K , AMU = 1.66E-27 kg

(a) Determine the root mean square velocity of the helium molecules.    m/s

(b) Determine the average molecular kinetic energy of the helium    J

(c) Determine the total thermal energy in the tank.    J

Explanation / Answer

part a:

root mean square velocity of helium molecule=sqrt(3*R*T/M)

where R=gas constant=8.315 J/(mol.K)

T=temperature=12 degree celcius=12+273=285 K

M=molar molecular mass=4.0026 grams

then root mean square velocity of helium molecule=sqrt(3*8.315*285/(4.0026*0.001))

=1332.7 m/s

part b:

average molecular kinetic energy=(3/2)*k*T

where k is boltzman;s constant

=(3/2)*1.38*10^(-23)*285

=5.9*10^(-21) J

part c:

given volume=11 m^3

temperature=285 K

pressure=1 atm=101325 N/m^2

then. number of moles=pressure*volume/(gas constant*temperature)

=470.39

so total energy=number of moles*number of molecules per mole*energy per molecule

=470.39*6.022*10^23*5.9*10^(-21)

=1.6713*10^6 J

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