A certain gas obeys PVm b RT The value of partial Z partial

Question

A certain gas obeys P(V_(m) - b) = RT. The value of ( partial Z / partial P )_T is xb / RT. The value of x is _________. (Integer answer) (Z : compressibility factor)

DivineJEE · Accepted Answer

For 1 mole of a real gas, the van der Waals' equation is,

\left( {p + {a \over {V_m^2}}} \right)({V_m} - b) = RT

At very high pressure, the equation becomes,

p({V_m} - b) = RT

\Rightarrow p{V_m} = RT + pb \Rightarrow {{p{V_m}} \over {RT}} = 1 + {{pb} \over {RT}}

\Rightarrow Z = 1 + {{pb} \over {RT}}

[

\because

Z = {{p{V_m}} \over {RT}}

= compressibility]

\therefore

{\left( {{{\delta Z} \over {\delta p}}} \right)_T} = 0 + {b \over {RT}} + {b \over {RT}} = {{xb} \over {RT}}

(Given)

\Rightarrow x = 1

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