Answer to Question #143115 in Mechanics | Relativity for emille

Question

How many particles are present in a closed container if the energy it contains is 93978.85 J, and the diatomic oxygen gas is moving at a velocity of 62.38m/s? Use only the whole number for the value of atomic mass unit. Express your answer in proper scientific notation.

Answer 1

$v=\sqrt{\frac{3kT}{m_0}},$

$E=\frac32NkT,$

$v=\sqrt{\frac{2E}{Nm_0}},$

$m_0=\frac{M}{N_A},$

$v=\sqrt{\frac{2EN_A}{NM}},$

$N=\frac{2EN_A}{v^2M},$

$N=\frac{2\cdot93978.85\cdot6.02\cdot10^{23}}{62.38^2\cdot32\cdot10^{-3}}=9.09\cdot10^{26}.$