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(iv) Rate of effusion of a gas: The rate of passing of a gas through an orifice may be given as:

$$r = \frac{PA}{\sqrt{2\pi RTm}}$$

where
$P = $ Partial pressure of the gas
$A = $ Area of cross-section of the orifice
$R = $ Gas constant
$T = $ Absolute temperature
$m = $ Molar mass of gas

I am unable to get two things straight:

  1. Shouldn't higher temperatures mean higher energy for the molecules and therefore a greater rate of effusion?
  2. Even if this is so, isn't absolute temperature the lowest temperature at which a gas can exist (zero volume) with a constant value corresponding to $\pu{-273.15 K}$?

Edit: I have resolved the first query, $P$ can be rewritten as $RT/V$ bringing the $\sqrt{T}$ term to the numerator. I am however still confused with what is meant by absolute temperature.

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  • $\begingroup$ Wrt question 1, this gives an answer. Wrt q2: you misunderstand the meaning of absolute temperature. $\endgroup$
    – Buck Thorn
    Commented Nov 14, 2019 at 8:20
  • $\begingroup$ But doesn't absolute temperature refer to absolute zero? $\endgroup$
    – John Tony
    Commented Nov 14, 2019 at 8:35
  • $\begingroup$ The absolute temperature scale defines an absolute zero which cannot be surpassed (unlike say Fahrenheit or Celsius, where negative temperatures are possible). $\endgroup$
    – Buck Thorn
    Commented Nov 14, 2019 at 8:37
  • $\begingroup$ So absolute temperature just means temperature in the Kelvin scale? $\endgroup$
    – John Tony
    Commented Nov 14, 2019 at 8:44
  • 1
    $\begingroup$ @JohnTony Yes, that's correct. $\endgroup$
    – Buck Thorn
    Commented Nov 14, 2019 at 8:59

1 Answer 1

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The equation can be rewritten by substituting P = RT/V from the Ideal Gas Equation. This gives us (A√RT/(V√2πm) showing that increase in temperature leads to increase in rate of effusion. Absolute Temperature simply refers to the temperature on the Kelvin scale of absolute temperature.

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  • $\begingroup$ is a check mark symbol that has nothing to do with a square root notation; this makes hard to read and parse your formulas. Please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown, or just have a closer look at the corrections done to your question and use the markup as an example. $\endgroup$
    – andselisk
    Commented Nov 14, 2019 at 9:19

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