Question

A liquid occupies half of a vessel at a particular temperature. The volume of the un occupied part remains constant at all temperature. If Alpha and gamma are the coefficient of linear and real expansion of a vessel and liquid,then gamma=n alpha then n value​

Answer 1

Volume expansion is given as,

Vf=Vi(1+3αΔT)

Here, Vf

is the final volume, Vi

is the initial volume, α

is the coefficient of linear expansion and ΔT

is the temperature change.

Complete step by step solution:

We assume at temperature T1

, the volume of the vessel is VV

and volume of liquid is VL

.

We have given that, VL=VV2

.

Since the volume of unoccupied part remains constant at any temperatures, we can write,

VV−VL=constant

…… (1)

We know that the coefficient of volume expansion is three times the coefficient of linear expansion. Therefore, we have, αV=3αL

, where, αL

is the coefficient of linear expansion.

Assuming the volume of the vessel at temperature T2

is V′V

and volume of liquid is V′L

.

We can express the volume expansion of vessel with temperature as follows,

V′V=VV(1+3αΔT)

…… (2)

Also, the volume expansion of liquid is,

V′L=VL(1+γΔT)

…… (3)