Question

When pressure of a gas (at ${20}^{\circ }\text{C}$ temperature) is changed from $P_1=1.01\times {10}^5\text{Pa}$ to $P_2=1.165\times {10}^5\text{Pa}$, the volume changes by $10$%. Then the bulk modulus of the gas is

• A. $1.55\times {10}^5\text{Pa}$
• B. $0.155\times {10}^5\text{Pa}$
• C. $1.4\times {10}^5\text{Pa}$
• D. $1.01\times {10}^5\text{Pa}$

Answer 1

The correct option is A $1.55\times {10}^5\text{Pa}$

Bulk modulus $B=\frac{\Delta P}{\frac{\Delta V}{V}}$
Here, $\Delta P=P_2-P_1=(1.165-1.01)\times {10}^5\text{Pa}=0.155\times {10}^5\text{Pa}$
and $\frac{\Delta V}{V}=\frac{10}{100}=0.1$

$\Rightarrow B=\frac{0.155\times {10}^5}{0.1}$
$\Rightarrow B=1.55\times {10}^5\text{Pa}$