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johnconnor
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Derive an expression for the number of impact of gas molecules on unit area in unit time in terms of the number of molecules per unit volume, n, and their mean speed, <c>. Explain the assumptions you make.
A disc of radius "a" rotates with constant angular velocity "omega" in a gas at low pressure so that the molecules of the gas strike the disc from random directions. If the molecules are momentarily attached to the disc and leave in random directions relative to the disc, derive an expression for the torque exerted on the disc by the gas in terms of <c>, the mean speed of the gas molecules, rho, the density of gas, "a" and omega.
The guide says such:
Whoa. Whadahell just happened? Is this something beyond a CIE A Level Physics student's reach?
A disc of radius "a" rotates with constant angular velocity "omega" in a gas at low pressure so that the molecules of the gas strike the disc from random directions. If the molecules are momentarily attached to the disc and leave in random directions relative to the disc, derive an expression for the torque exerted on the disc by the gas in terms of <c>, the mean speed of the gas molecules, rho, the density of gas, "a" and omega.
The guide says such:
The Joule classification of velocities is normally acceptable at this level of application of the kinetic theory of gases. Quite by chance, the Joule classification does lead to the correct numerical factor (1/3) in the formula for the pressure of a gas but it does not give the correct factor for the number of molecules striking unit area in unit time. The Joule classification gives n<c>/6 whereas the correct expression is n<c>/4. Try working out the correct expression by first considering those molecules in a hollow cone of angle between θ and (θ+ ∂θ) and then integrating over all values of θ from 0 to ∏/2 rad.
Whoa. Whadahell just happened? Is this something beyond a CIE A Level Physics student's reach?