Answer

Verified

68.7k+ views

**Hint:**Compressibility factor is also known as gas deviation factor. This is a correction factor which describes the deviation of real gas from ideal gas.

**Complete step by step answer:**

The real gases obey the ideal gas equation $(PV = nRT)$ only if pressure is low or temperature is high.

Van der waals equation for one mole of Real gas is given by

$\Rightarrow \left[ {p + \dfrac{q}{{{V^2}}}} \right]\left[ {V - b} \right] = RT$ . . . . . (1)

And for $n$ moles of gas

$\Rightarrow \left[ {p + \dfrac{q}{{{V^2}}}} \right]\left[ {V - nb} \right] = RT$

Where ‘a’ and ‘b’ are constants and called Van der Waals constants. Their values depend upon the nature of gas.

At high pressure $\dfrac{a}{{{V^2}}}$ can be neglected.

$\therefore $equation (1) becomes

$\Rightarrow P[v - b] = RT$

$\Rightarrow PV - Pb = RT$. . . . . (2)

Dividing equation (2) by $RT$ we get

$\Rightarrow \dfrac{{PV}}{{RT}} - \dfrac{{Pb}}{{RT}} = 1$

$\Rightarrow \dfrac{{PV}}{{RT}} = 1 + \dfrac{{Pb}}{{RT}}$ . . . . . (3)

$\Rightarrow Z = \dfrac{{PV}}{{RT}}$ . . . . . (4)

$\Rightarrow Z = 1 + \dfrac{{Pb}}{{RT}}$

Where $Z$ = compressibility factor

Therefore, at high pressure compressibility factor is $1 + \dfrac{{Pb}}{{RT}}$

**Therefore, by the above explanation, the correct option is [A] $1 + \dfrac{{Pb}}{{RT}}$**

**Additional information:**

At high pressure, compressibility factor is greater than $1$.

As $P$ is increased (at constant T). The factor $\dfrac{{Pb}}{{RT}}$ increases. This explains how compressibility increases continuously with pressure.

Van der Waals constants $a$ and $b$ have significance of attractive force among molecules of gas and value of $b$ is a measure of the effective size of gas molecules.

**Note:**A gas which obeys the ideal gas equation $PV = nRT$ under all conditions of temperature and pressure is called ideal gas. Concept of ideal gas is only theoretical when pressure is low and temperature is high. They obey the gas law. Such gases are known as Real gases. All gases are Real gases.

Recently Updated Pages

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

A man stands at a distance of 250m from a wall He shoots class 9 physics JEE_Main