An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100 kpa, the absolute pressure at the bottom of lake in kpa is ... (assume no temperature variation):

Question

An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100 kpa, the absolute pressure at the bottom of lake in kpa is ... (assume no temperature variation): (A) 33.3 (B) 50.0 (C) 100.0 (D) 300.0

Tardigrade Admin · Accepted Answer

In an isothermal change temperature remains constant.
For isothermal change

P V = RT =

constant
where,

P = h ρ g =

height

\times

density

\times

gravity

∴ P_{1} V_{1} = P_{2} V_{2}

Given,

V_{2} = 3 V_{1}, P_{2} = 100 k P a = 100 \times 1 0^{3} P a

∴ P_{1} = \frac{P _{2} V _{2}}{V _{1}}

= \frac{100 \times 1 0 ^{3} \times 3 V _{1}}{V _{1}} = 300 k P a

Q. An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100kpa, the absolute pressure at the bottom of lake in kpa is ... (assume no temperature variation):

33.3

50.0

100.0

300.0

In an isothermal change temperature remains constant. For isothermal change PV=RT= constant where, P=hρg= height × density × gravity ∴P1​V1​=P2​V2​ Given,V2​=3V1​,P2​=100kPa=100×103Pa ∴P1​=V1​P2​V2​​ =V1​100×103×3V1​​=300kPa

Q. An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is $100 k p a$ , the absolute pressure at the bottom of lake in $k p a$ is ... (assume no temperature variation):