InterviewSolution
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InterviewSolution
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Using the Maxwell distribution function, determine the pressure exterted by gas on a wall, if the gas temperature is `T` and the concentration of molecules is `n`. |
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Answer» Let, `dn(v_x) = n ((m)/(2 pi k T))^(1//2) e^(-mv_x^2//2 kT) dv_x` be the number of molecules per unit volume with `x` component of velocity in the range `v_x` to `v_x + dv_x` Then `p = int_0^oo 2mv_x.v_x dn(v_x)` =`int_0^oo 2 mv_x^2 n((m)/(2 pi kT))^(1//2) e^(-mv_x^2//2 kT) dv_x` =`2mn (1)/(sqrt(pi)) (2kT)/(m) int_0^oo u^2 e^(-u^2) du` =`(4)/(sqrt(pi)) nkT. int_0^oo x ^(-x) (dx)/(2 sqrt(x)) = nkT`. |
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