Question:
A bubble of an ideal gas rises from the bottom of a lake to the surface. At the bottom, the pressure is 3 Atm. and the temperature is 7 °C. At the surface, the pressure is 1 atm. and the temperature is 27 °C. If the initial volume of the bubble was $V_0$ what is its volume $V_f$ at the surface?
A bubble of an ideal gas rises from the bottom of a lake to the surface. At the bottom, the pressure is 3 Atm. and the temperature is 7 °C. At the surface, the pressure is 1 atm. and the temperature is 27 °C. If the initial volume of the bubble was $V_0$ what is its volume $V_f$ at the surface?
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Always convert Celsius to Kelvin in gas law problems by adding 273.
Updated On: May 5, 2026
- $3 V_0$
- $3.21 V_0$
- $0.9 V_0$
- $5.4 V_0$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Use the combined gas law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$.
Step 2: Meaning
Convert temperatures to Kelvin: $T_1 = 7 + 273 = 280$ K and $T_2 = 27 + 273 = 300$ K.
Step 3: Analysis
$V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} = V_0 \times \frac{3}{1} \times \frac{300}{280}$. $V_2 = V_0 \times 3 \times 1.071 = 3.21 V_0$.
Step 4: Conclusion
The volume at the surface is $3.21 V_0$.
Final Answer: (B)
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