Question

The pressure of a medium is changed from $1.01 \times 10^{5} \, \text{P} \text{a}$ to $1.165 \times 10^{5} \, \text{P} \text{a}$ and change in volume is $10 \%$ keeping temperature constant.The bulk modulus of the medium is

• A. $204.8 \times 10^{5} \, \text{P} \text{a}$
• B. $102.4 \times 10^{5} \, \text{P} \text{a}$
• C. $51.2 \times 10^{5} \, \text{P} \text{a}$
• D. $1.55 \times 10^{5} \text{P} \text{a}$

Answer 1

Answer: (D)

From the definition of bulk modulus,
$\beta =-\frac{\Delta P}{\Delta V / V}=-V\cdot \frac{\Delta P}{\Delta V}$
Substituting the values, we have
$\beta = \frac{- \left(\right. 1.165 - 1.01 \left.\right) \times \left(10\right)^{5}}{- 10} \times 100 = 1.55 \times \left(10\right)^{5 \, } \, Pa$