1My logic might be wrong ... IF LOGIC IS WRONG ... PLEASE MEREKO GALI MAT DENA ... YEHI SAMAJ LENA KI MERE DIMAG ME CHEMICAL LOCHA HAI . So please get it verified by NISHANT SIR ....
A horizontal tube, open at both ends, contains a column of liquid. the length of the liquid column does not change with temperature. Let γ = coefficient of volume expansion of the liquid and α= coefficient of volume expansion of the material of the tube.
1. γ = α
2. γ = 2α
3. γ = 3α
4. γ = 0
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8 Answers
1The case is actually like this ....
The volume of the liquid begins to increase followed by a rise in the level of liquid in the liquid column .... but the rise in level is not visible as the increase of volume of the cylinder is occurring simultaneously ....
[ radius of the cylinder is increasing. ]
If we consider the initial volume of liquid in liquid column as Î r2h ... where r is initial radius of cylinder and h is the initial and final level of liquid ...
Then for expansion of liquid ....
Πr12h = Πr2h(1 + γΔt) ... (1) ...where r1 is the final radius of the cylinder ...
For expansion of cylinder ...
Πr12h = Πr2h(1 + αΔt) ... (2) ... where we are considering the volume expansion for only h length of the cylinder.
The liquid takes up the shape of the cylinder ... So both have same final volume for h length ...
Solving (1) and (2) ...
γ = α
1
62There is a mistake ARKA..
What you have to consider is the change in radius and thus the change in cross section area should equate to othe change in volume of liquid...
1but after binomial approx. the answer is same!!!
Am i doing mistake some where??
Plz post the solution!!!
1Sir ... if we consider the increase in cross section .... then we have to put coefficient of expansion of area as 2α .... and get ans as γ = 2α
But that can be only possible in case of a cubical container .... How can we put that fact here ???!!!
1Sorry ... sorry sir ... I was wrong with my third post ...
But I'm still having doubt with the equations ...
1yes nishant bhaiya ur rite it will expand cross sectionally but wont it also expand in the vertical direction