Question

A given quantity of an ideal gas is at the pressure $P$ and the absolute temperature $T$ . The isothermal bulk modulus of the gas is

• A. $\frac{2}{3}P$
• B. $P$
• C. $\frac{3}{2}P$
• D. $2P$

Answer 1

Answer: (B)

$\because $ $\beta =\frac{\Delta P}{\frac{\Delta V}{V}}$
$\therefore $ In the isothermal process $\left(P + \Delta P\right) \, \left(V - \Delta V\right)=PV$
or $PV-P\Delta V+V\Delta P-\Delta P\Delta V=PV$
But $\Delta P \, \Delta V$ maybe neglected.
$\therefore \, $ $V \, \Delta P=P \, \Delta V$
or $\frac{\Delta P}{\frac{\Delta V}{V}}=P$
Hence, ( $P$ ) is correct.