Which of the following graphs correctly represents the variation of `beta=-(dV//dP)/V`
with P for an ideal gas at constant temperature?

Options

A.
B.
C.
D.

Answer

A

Explanation

At a constant temperature, for a given mass of gas, PV=constant, according to Boyle's law
`therefore PV=`constant `thereforePdV+VdP=0`
or `(dV)/(dP)=-(V)/(P) or -(dV)/(VdP)=+(1)/(P)`
or `beta=(1)/(P)` or `betaP=1`
The equation between `beta` and P is of the form xy=constant which represents a rectangular hyperbola.
`therefore` Graph between `beta` and P will be a rectangular hyperbola represented by graph (a)