Properties of Matter 1 Question 13
13. A given quantity of an ideal gas is at pressure $p$ and absolute temperature $T$. The isothermal bulk modulus of the gas is
(a) $\frac{2}{3} p$
(b) $p$
(c) $\frac{3}{2} p$
(d) $2 p$
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Answer:
Correct Answer: 13. $\frac{1}{2}\left(\frac{Y A}{L}\right) x^{2}$
Solution:
- In isothermal process
$$ \begin{aligned} & p V=\text { constant } \\ & \therefore \quad p d V+V d p=0 \quad \text { or }\left(\frac{d p}{d V}\right)=-\left(\frac{p}{V}\right) \\ & \therefore \text { Bulk modulus, } B=-\left(\frac{d p}{d V / V}\right)=-\left(\frac{d p}{d V}\right) V \\ & \therefore \quad B=-\left[\left(-\frac{p}{V}\right) V\right]=p \\ & \therefore \quad B=p \end{aligned} $$
NOTE Adiabatic bulk modulus is given by $B=\gamma P$.
