I am having a problem in differentiating between the two types of problems given below and also am unable to understand why they give different answers. PLEASE SOMEONE HELP. 1) A long cylindrical vessel having coefficient of linear expansion , is filled with a liquid upto a certain level. On heating it is found that level of liquid in cylinder remains the same. What is the relation between the coefficient of volume expansion of the liquid and the coefficient of linear expansion of the vessel. ( Ans : = 3 ) Solution given : As there is no apparent expansion, from the relation , So, 2) A horizontal tube open at both ends having coefficient of linear expansion , contains a column of a liquid of a certain length. On heating it is found that lenght of liquid column in the tube remains the same. What is the relation between the coefficient of volume expansion of the liquid and the coefficient of linear expansion of the tube. ( Ans : = 2 ) Solution given : V t = l.A t . or, V 0 .( 1 + t ) = l.A 0 .( 1 + t ) or l.A 0 .( 1 + t ) = l.A 0 .( 1 + 2 t ) or = 2 . ------------------------------------------------------------------------------------------------------------------------------------------------- Why cant we interchange the concepts used in both the questions ? If done so, we'll get interchanged answers !! Further is it possble to write when the liquid does not occupy almost full volume of the vessel ? I am asking this as its derivation involves the following step - . PLEASE ANSWER.

I am having a problem in differentiating between the two types of problems given below and also am unable to understand why they give different answers. PLEASE SOMEONE HELP.

1) A long cylindrical vessel having coefficient of linear expansion , is filled with a liquid upto a certain level. On heating it is found that level of liquid in cylinder remains the same. What is the relation between the coefficient of volume expansion  of the liquid and the coefficient of linear expansion  of the vessel. 

( Ans :   = 3 )

Solution given : As there is no apparent expansion, from the relation ,

So,  

 

2) A horizontal tube open at both ends having coefficient of linear expansion , contains a column of a liquid of a certain length. On heating it is found that lenght of liquid column in the tube remains the same. What is the relation between the coefficient of volume expansion  of the liquid and the coefficient of linear expansion  of the tube. 

( Ans :   = 2 )

Solution given : V_t = l.A_t .

or, V₀.( 1 + t )  = l.A₀.( 1 + t )

or l.A₀.( 1 + t ) = l.A₀.( 1 + 2t )

or  = 2.

-------------------------------------------------------------------------------------------------------------------------------------------------

Why cant we interchange the concepts used in both the questions ? If done so, we'll get interchanged answers !!

Further is it possble to write  when the liquid does not occupy almost full volume of the vessel ?

 I am asking this as its derivation involves the following step -

.

PLEASE ANSWER.