Which of the following graphs correctly represents the variation of `beta = -((dV)/(dP))(1)/(V)` with P for an ideal gas at constant temperature ?

Options

A.
B.
C.
D.

Answer

A

Explanation

For an ideal gas, the differential form of gas law is `VdP + PdV = nRdT`
At constant temperature dT = 0
`rArr VdP + PdV = 0`
`PdV = -VdP`
`(-dV)/(dP) = ((V)/(P))` or `-((dV)/(dP)) (1)/(V) = (1)/(P) rArr beta = (1)/(P)`
`beta P` = constant
Hence the graph could be a rectangular hyperbola as shown in (a).