Question

A bubble of volume $V_{1}$ is present in the bottom of a pond at $15^{\circ} C$ and $1.5 atm$ pressure. When it comes at the surface, it observes a pressure of 1 atm at $25^{\circ} C$ and has volume $V_{2}$. The value of $V_{2} / V_{1}$ is

• A. $15.5$
• B. $0.155$
• C. $155.0$
• D. $1.55$

Answer 1

Answer: (D)

$p_{1}=1.5$ atm , $T_{1}=15^{\circ} C =(15+273) K =288 K$
$p_{2}=1$ atm , $T_{2}=25^{\circ} C =(25+273)=298 K$
According to combined gas law,
$\frac{p_{1} V_{1}}{T_{1}} =\frac{p_{2} V_{2}}{T_{2}} $
$\Rightarrow \frac{p_{1} T_{2}}{T_{1} p_{2}} =\frac{V_{2}}{V_{1}} $
$\Rightarrow \frac{V_{2}}{V_{1}} =\frac{1.5 \times 298}{288 \times 1}=1.55 $