States of Matter - Result Question 9
####9. A bubble of air is underwater at temperature $15^{\circ} C$ and the pressure $1.5 bar$. If the bubble rises to the surface where the temperature is $25^{\circ} C$ and the pressure is $1.0 bar$, what will happen to the volume of the bubble?
[2011M]
(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.
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Solution:
- (a) Given
$P_1=1.5$ bar, $T_1=273+15=288 K, V_1=V$
$P_2=1.0$ bar, $T_2=273+25=298 K, V_2=$ ?
$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$
$\frac{1.5 \times V}{288}=\frac{1 \times V_2}{298}$
$V_2=1.55 V$ i.e., volume of bubble will be almost 1.6 time to initial volume of bubble.
