MCQ
Under isothermal condition, the pressure of a gas is given by $P = aV ^{-3}$, where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to $..........\,P$
- A$0.5$
- ✓$3$
- C$2$
- D$1$
✓
Answer
Correct option: B.
$3$
b
$B =-\frac{ dP }{ dv / v }$
$B =-\frac{ dP }{ dv / v }$
$Pv ^3= a$
Differentiating w.r.t to pressure
$v^3+P 3 v^2 \frac{d v}{d P}=0$
$v=-3 \frac{P d v}{d P}=0$
$v=-3 \frac{P d v}{d P}$
$\frac{d P . v}{d v}=-3 P$
$B=-\left(\frac{d P v}{d v}\right)=-(-3 P)=3 P$
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