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Which of the following graphs correctly ...

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

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
B
At constant temperature, PV = constant
On differentiation, we get `PdV+VdP=0`
or `(dV)/(dP)=-(V)/(P)or-(dV)/(VdP)=(1)/(P)orbeta=(1)/(P)orbetaP=1`
The equation between `betaandP` is of the form xy = constant which represents a rectangular hyperbola.
Thus, the graph between `betaandP` will be a rectangular hyperbola and it is represented by (a).
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