10^{23} molecules of a gas, each having a mas | vedclass

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(D) The change in momentum of one molecule striking the wall and rebounding is given by $\Delta p = 2mv \cos 	heta$, where $m$ is the mass, $v$ is th

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$1500$

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(D) The change in momentum of one molecule striking the wall and rebounding is given by $\Delta p = 2mv \cos 	heta$, where $m$ is the mass, $v$ is the velocity, and $	heta$ is the angle with the normal.Given: $m = 3 	imes 10^{-27} \,kg$, $v = 500 \,m/s$, $	heta = 60^{\circ}$, $N = 10^{23}$ molecules/sec, and $A = 1 \,cm^2 = 10^{-4} \,m^2$.Pressure $P = \frac{F}{A} = \frac{1}{A} 	imes \frac{\Delta p}{\Delta t} = \frac{N 	imes (2mv \cos 60^{\circ})}{A}$.Substituting the values: $P = \frac{10^{23} 	imes 2 	imes (3 	imes 10^{-27}) 	imes 500 	imes \cos 60^{\circ}}{10^{-4}}$.Since $\cos 60^{\circ} = 0.5$, we have $P = \frac{10^{23} 	imes 6 	imes 10^{-27} 	imes 500 	imes 0.5}{10^{-4}} = \frac{3000 	imes 10^{-4} 	imes 0.5}{10^{-4}} = 1500 \,N/m^2$.

$10^{23}$ molecules of a gas, each having a mass of $3 \times 10^{-27} \,kg$, strike per second per $cm^2$ of a rigid wall at an angle of $60^{\circ}$ with the normal and rebound with a velocity of $500 \,m/s$. The pressure exerted by the gas molecules on the wall is: (in $\,N/m^2$)

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