An air bubble at the bottom of a lake has a volume of 20 \(cm ^{3}\), pressure of \(4.9 Pa\), and temperature \(4^{\circ} C\). The bubble rises to the surface where the temperature is \(20^{\circ} C\) and the pressure \(1.0 Pa\). Find the volume as the bubble reaclies the surface. (Take \(1 atm =1,0 \times 10^{5} N / m ^{2}\) ).
A. \(124 cm ^{3}\) B. 319 \(cm ^{3}\) C. \(60 cm ^{3}\) D. \(104 cm ^{3}\)
Correct Answer: D
Explanation
given: \(V_{1}=20 cm ^{3}, P_{1}=4.9 Pa\), \(T_{1}=4^{\circ} C =277 K\) \(T_{2}=20^{\circ} C +273=293 K ; P_{2}=1.0 Pa\), required \(V_{2}=\) ? Using the ideal gas equation, $$ \begin{aligned} \frac{P_{1} V_{1}}{T_{1}} &=\frac{P_{2} V_{2}}{T_{2}} ; V_{2}=\frac{P_{1} V_{1} T_{2}}{P_{2} T_{1}} \\ &=\frac{4.9 \times 20 \times 293}{1.0 \times 277} \\ &=103.66 cm ^{3} \approx 104 cm ^{3} \\ V_{2} &=104 cm ^{3} \end{aligned} $$
