Question

A bubble of gas is released from the mud at the bottom of the pond. Its initial volume is 0.5
cm3
.
Ignoring any temperature differences in the water,
Calculate the volume of the bubble as it reaches the surface.

Answer 1

A bubble of gas is released from the mud at the bottom of the pond. Its initial volume is 0.5 cm³.

Now, as the question says that :

• The temperature differences have to be neglected, it means that the process is ISOTHERMAL.

• Let atmospheric pressure be P_(0) and height of pond be h.

For isothermal processes, we can say :

$P_{1}V_{1} = P_{2}V_{2}$

$\implies (P_{0} + \rho gh)0.5 =(P_{0})V_{2}$

$\implies V_{2} = \dfrac{(P_{0} + \rho gh)0.5}{P_{0}}$

So, final volume of bubble will be :

$\boxed{V_{2} = \dfrac{(P_{0} + \rho gh)0.5}{P_{0}}}$