Question

The pressure of a fixed mass of air is $1.01\times {10}^{5}Pa.$ It is compressed slowly, keeping its temperature constant. Then bulk modulus of air is,

• A. $1.414\times {10}^5$pa.
• B. $1.67\times {10}^5$pa.
• C. $51.2\times {10}^5$pa.
• D. $1.01\times {10}^5$pa.

Answer 1

Answer: (D)

$1.01\times {10}^5$pa.

$\begin{array}{c}P=1.01\times {10}^{5}Pa\\ \text{Temperature is constant}\Rightarrow \text{isothermal process}\end{array}$

$\begin{array}{cc}& PV=\text{constant}\\ \Rightarrow & P\left(\Delta V\right)+\left(\Delta P\right)\left(V\right)=0\\ \Rightarrow & \frac{\Delta V}{V}=-\frac{\Delta P}{P}⟶\left(1\right)\\ B& =\frac{-\Delta P}{\Delta V/V}⟶\text{(2)}\end{array}$

$\begin{array}{c}\Rightarrow B=P⟶\text{using}\left(1\right)\\ \Rightarrow B=1.01\times {10}^{5}Pa\\ \text{Ans :}\left(D\right)\end{array}$