Respuesta :
Answer :
The average kinetic energy is, [tex]7.659\times 10^{-21}J[/tex]
The root mean square speed is, [tex]679.02m/s[/tex]
Explanation:
(a) The formula for average kinetic energy is:
[tex]K.E=\frac{3}{2}kT[/tex]
where,
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature = 370 K
Now put all the given values in the above average kinetic energy formula, we get:
[tex]K.E=\frac{3}{2}\times (1.38\times 10^{-23}J/K)\times (370K)[/tex]
[tex]K.E=7.659\times 10^{-21}J[/tex]
The average kinetic energy is, [tex]7.659\times 10^{-21}J[/tex]
(b) The formula used for root mean square speed is:
[tex]\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
[tex]\nu_{rms}[/tex] = root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature = 370 K
M = atomic mass = 0.02 kg/mole
[tex]N_A[/tex] = Avogadro’s number = [tex]6.02\times 10^{23}mol^{-1}[/tex]
Now put all the given values in the above root mean square speed formula, we get:
[tex]\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (370K)}{0.02kg/mol}}[/tex]
[tex]\nu_{rms}=679.02m/s[/tex]
The root mean square speed is, [tex]679.02m/s[/tex]
