Q: An aluminium can of cylindrical shape contains 500 cc of water. The area of cross section of the can is 125 cm². All measurements refer to 10^oC. Find the rise in water level if temp increases to 80^oC.

The coefficient of linear expansion of aluminium = 23 x 10 ^-6/^oC and average coefficient of volume expansion of water = 3.2 x 10 ^-4/^oC

Answer : 0.089cm

Its an HCV question.

Can u arrive at the given answer ??

A probable solution can be this -

_aluminium = 2_aluminium = 2 ( 23 x 10 ^-6 ) = 4.6 x 10 ^-5.

A_t = A₀.( 1 + _aluminium t )

= 125. ( 1 + 4.6 x 10 ^-5.70) = 125.4025 cm².

And V_t = V₀. { 1 + (_apparent ).t }

or V_t = V₀. { 1 + (_water - _vessel ).t }

= 500. { 1 + ( 3.2 x 10 ^-4 - 3 x 23 x 10 ^-6 ).70 }

= 508.785

So, l_t = V_t / A_t . = 508.785 / 125.4025 = 4.057.

and initial length = 500/125 = 4cm.

So rise = 4 - 4.057 = 0.057cm.

Did u see ?? The answer is so different.

But yes, if we take real expansion of water and neglect expansion of vessel, the answer exactly matches.

But why should we do so??

Rise in water level => final level - initial level = apparent increase in length..

And why should the vessel not expand ??

PLEASE HELP !!!!

Jitender Pal , 11 Years ago

Grade 9