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?
(a) Volume will become greater by a factor of 1.6.
(b) Volume will become greater by a factor of 1.1.
(c) Volume will become smaller by a factor of 0.70.
(d) Volume will become greater by a factor of 2.5.
Correct answer: (a) Volume will become greater by a factor of 1.6.
Explanation:
Given
P1 = 1.5 bar, T1 = 273 + 15 = 288 K, V1 = V
P2 = 1.0 bar ,T1 = 273 + 25 = 298K, V2 = ?
\(\frac{P_1V_1}{T_1}\) = \(\frac{P_2V_1}{T_2}\)
\(\frac{1.5 \times V}{288}\) = \(\frac{1 \times V_2}{298}\)
V2 = 1.55 V i.e., volume of bubble will be almost 1.6 time to initial volume of bubble.