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Q: An aluminium can of cylindrical shape contains 500 cc of water. The area of cross section of the can is 125 cm 2 . All measurements refer to 10 o C. Find the rise in water level if temp increases to 80 o C. The coefficient of linear expansion of aluminium = 23 x 10 -6 / o C and average coefficient of volume expansion of water = 3.2 x 10 -4 / o C 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 = A 0 .( 1 + aluminium t ) = 125. ( 1 + 4.6 x 10 -5 .70) = 125.4025 cm 2 . And V t = V 0 . { 1 + ( apparent ).t } or V t = V 0 . { 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 !!!!


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 10oC. Find the rise in water level if temp increases to 80oC.


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


At = A0.( 1 + aluminium t )


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


 


And Vt = V0. { 1 + (apparent ).t }


or Vt = V0. { 1 + (water - vessel ).t }


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


= 508.785


 


So, lt = Vt / At . = 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 !!!!


Grade:9

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