Updated spacing between @ latex expressions

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правка #10452 предыдущая #10178 GitHub c702ebe ← раньше
en/5.6.22.md +3 −3
@@ -86,14 +86,14 @@
Substituting $(5)$ and $(7)$ into $(3)$ and separating $v$
$$\boxed{v = \sqrt{2gH\left(1-\frac{PS}{Mg}+\frac{PS}{Mg}\ln{\frac{PS}{Mg}}\right)}}$$
b) From Poisson's Law
− $$P(SH)^\gamma = P'(Sy)^\gamma \quad(8)$$
+ $$P(SH)^\gamma = P'(Sy)^\gamma\quad(8)$$
The work done by the gas in an adiabatic process is given by
− $$A = \frac{PSH-P'Sy}{\gamma-1} \quad(9)$$
+ $$A = \frac{PSH-P'Sy}{\gamma -1} \quad(9)$$
According to $(6)$, we can modify $(8)$ and separating $y$, obtaining
$$y = H\left(\frac{PS}{Mg}\right)^\frac{1}{\gamma} \quad(10)$$
Putting $(9)$ into $(1)$, and taking account $(6)$,
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− $$\frac{Mv^2}{2} = H\left(Mg+\frac{PS}{\gamma-1}\right)-Mgy\left(1+\frac{1}{\gamma-1}\right) \quad(11)$$
+ $$\frac{Mv^2}{2} = H\left(Mg+\frac{PS}{\gamma -1}\right)-Mgy\left(1+\frac{1}{\gamma -1}\right) \quad(11)$$
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Substituting $(10)$ into $(11)$, since gas is monoatomic ($i = 3$ and $\gamma = 5/3$), and separating $v$
$$\boxed{v = \sqrt{2gH\left[1-\frac{5}{2}\left(\frac{PS}{Mg}\right)^\frac{3}{5}+\frac{3}{2}\frac{PS}{Mg}\right]}}$$
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