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A bubble of air is underwater at temperature 15°C and the pressure 1.5 bar. If the bubble rises to the surface where the temperature is 25°C and the pressure is 1.0 bar, what will happen to the volume of the bubble?

1. Volume will become greater by a factor of 1.6.
2. Volume will become greater by a factor of 1.1.
3. Volume will become smaller by a factor of 0.70.
4. Volume will become greater by a factor of 2.5.

Correct answer: Volume will become greater by a factor of 1.6.

Solution

Using the combined gas law, \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \), we calculate the volume change. Converting temperatures to Kelvin: \( T_1 = 15 + 273 = 288 \, K \), \( T_2 = 25 + 273 = 298 \, K \). Substituting \( P_1 = 1.5 \), \( P_2 = 1.0 \), and solving for \( V_2/V_1 \), the factor is approximately 1.6.

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