Solution:
The condition of state is given by,
![\[\begin{array}{*{35}{l}} pV\text{ }=\text{ }nRT\text{ }\ldots \text{ }..\left( 1 \right) \\ ~ \\ Where,\text{ }p\text{ }=\text{ }pressure \\ ~ \\ V\text{ }=\text{ }volume \\ ~ \\ N\text{ }=\text{ }number\text{ }of\text{ }moles \\ ~ \\ R\text{ }=\text{ }Gas\text{ }steady \\ ~ \\ T\text{ }=\text{ }temp \\ ~ \\ n/V=P/RT \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-16e023a50c5c9fe6a117ce72069a2191_l3.png "Rendered by QuickLaTeX.com")
Supplant n with m/M
, thusly,
![\[\begin{array}{*{35}{l}} m/V=p/RT...........\left( 2 \right) \\ ~ \\ Where\text{ }m=mass \\ ~ \\ M=\text{ }molar\text{ }mass \\ ~ \\ In\text{ }any\text{ }case,\text{ }m/V\text{ }=\text{ }d \\ ~ \\ Where,\text{ }d\text{ }=\text{ }thickness \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-094dcecdf44bfbc19cf0fba584f91a99_l3.png "Rendered by QuickLaTeX.com")
Thusly, from condition (2), we get
![\[\begin{array}{*{35}{l}} d/M=p/RT \\ ~ \\ d=\left( M/RT \right)P \\ ~ \\ d\propto p \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c0742272a056e472ac54e92bcff289ee_l3.png "Rendered by QuickLaTeX.com")
Thusly, at a given temp, the thickness of the gas (d) is relative to its tension (p).
sing the condition of state pV=nRT; show that at a given temperature thickness of a gas is corresponding to gas pressure p.
sing the condition of state pV=nRT; show that at a given temperature thickness of a gas is corresponding to gas pressure p.