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

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

NTA AbhyasNTA Abhyas 2022

Solution:

In the isothermal process
$PV =$ constant
$\therefore P d V+V d P=0$ or $\left(\frac{ d P}{ d V}\right)=-\left(\frac{P}{V}\right)$
$\therefore$ Bulk modulus, $B=-\left(\frac{ d P}{ d V / V}\right)=-\left(\frac{ d P}{ d V}\right) V$
$\therefore B=-\left[\left(-\frac{P}{V}\right) V\right]=P$
$\therefore B=P$
Note: Adiabatic bulk modulus is given by $B=\gamma P$