Question

the diameter of a bubble at a surface of lake is 4mm and the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm and the temperature of lake water and atmosphere are equal. What is the depth of the lake?(The density of lake water and hg are 1 gm/ml and 13.6 gm/ml respectively, also neglect the contribution of pressure due to surface tension)

Answer 1

Answer:We know from the Charles Law that the pressure is directly proportional to the temperature at a given volume.

So, we get that  

T  

1

​  

 

P  

1

​  

V  

1

​  

 

​  

=  

T  

2

​  

 

P  

2

​  

V  

2

​  

 

​  

 

Case1- When the bubble is at surface.

The pressure is P  

1

​  

=1atm

And the volume is V  

1

​  

=4π×(4)  

2

 

Case2- When the bubble is at the bottom then we will get that.

The pressure will be P2=1atm+ρgh which will be (1+  

10  

5

 

1000×9.8×h

​  

)atm

The volume is V  

2

​  

=4π1  

2

 

Since, the temperature is same given in the question, so on substituting the values in the equation we will get.

16=1+0.098h

On solving we will get h=153.03m