A sample of gas follows process represented by $$PV^2 = constant$$. Bulk modulus for this process is B, then which of the following graph is/are correct?
$$P{ V }^{ 2 }= consatnt $$
VP2=constant⇒P∝V2⇒ΔPP=−2ΔVV⇒
on differentiating, $$dP=-2VdV$$
Bulk modulus $$B$$ =$$\dfrac { -1 }{ V } \dfrac { dP }{ dV } = 2P$$
$$B$$ is directly proportional to Pressure $$P$$.
Hence, option A is correct
Bulk modulus $$B$$ =$$\dfrac { -1 }{ V } \dfrac { dP }{ dV } $$=C/{ V }^{ 2 }$$
$$C$$=constant
Hence,option B is correct
Using ideal gas equation, $$PV=nRT$$
since $$B \propto \dfrac { 1 }{ { V }^{ 2 } } $$ implies
$$B\propto { T }^{ 2 }$$
Hence, option C is correct
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