Question

If the pressure of gas is increased from $1.01\times {10}^{5}Pa$ to $1.165\times {10}^{5}Pa$ and volume is decreased by 10$\%$ at constant temperature, then bulk modulus of the gas is

• A. $15.5\times {10}^{5}Pa$
• B. $1.4\times {10}^{15}Pa$
• C. $1.55\times {10}^{5}Pa$
• D. $0.0155\times {10}^{5}Pa$

Answer 1

Answer: (C)

$1.55\times {10}^{5}Pa$

$\begin{array}{c}\text{Given,}\\ \text{Pressure of gas increased from}1.01\times {10}^5\text{to}1.165\times {10}^5\\ \text{So,}△P\text{(change in Pressure)}=(1.165-1.01)\times {10}^5{P}_a\end{array}$

$\Delta P=0.155\times {10}^{5}Pa$

$\begin{array}{c}\\ \frac{\Delta V}{V}\times 100=-10(-)\text{( sign represent}\\ \text{decreased in volume)}\\ \frac{\Delta V}{V}=\frac{-10}{100}\end{array}$

$\begin{array}{c}\text{we know,}\\ \begin{array}{cc}\beta ulk\text{modulus}\left(B\right)& =\frac{\Delta P}{\left(\frac{\Delta V}{V}\right)}\\ \beta & =\frac{0.155\times {10}^5}{\left(\frac{10}{100}\right)}\\ \beta & =1.55\times {10}^{5}Pa\end{array}\end{array}$