Ideal gas equation is represented as `PV=nRT`. Gases present in universe were fond ideal in the Boyle's temperature range only and deviated more from ideal gas behavior at high pressure and low temperature.
The deviation are explained in term of compressibility factor `z`. For ideal behavior `Z=(PV)/(nRT)=1`. the main cause to show deviavtion were due to wrong assumptions made about forces oif attractions (which becomes significant at high pressure ) and volume `V` occupied by molecules in `PV=nRT` is supposed to be volume of gas or the volume of container in which gas is placed by assuming that gaseous molecules do not have appreciable volume. Actually volume of the gas is that volume in which each molecule of gas can move freely. If volume occupied by gaseous molecule is not negligible, then the term `V` would be replaced by the ideal volume which by available for free motion of each molecule of gas in 1 mole gas.
`V_("actual")=` volume of container -volume occupied by molecules
`=v-b`
Where `b` represent the excluded volume occupied by molecules present in one mole of gas.
Similarly for `n` mole gas
`V_("actual")=v-nb`
The ratio of coefficient of thermal expansion `alpha=(((delV)/(delT))_(P))/V` and the isothermal compressibility
`beta=-((delV)/(delP)_(T))` for an ideal gas is:

Options

A. `-P/T`
B. `P/T`
C. `T/P`
D. `-T/P`

Answer

B

Explanation

`PV=RT` (for 1 mole of gas)
`:.PdelV=RdelT`
or `((delV)/(delT))_(P)=R/P =(R.V)/(RT)`
or `alpha=(((delV)/(delT))_(P))/V=1/T`
`P.delV+V.delP=0`
`((delV)/(delP))_(T)=-V/P`
Also or `beta=-(((delV)/(delP))_(T))/V=1/P`
`(alpha)/(beta)=P/T`