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An iron rod of length 50 cm is joined at...

An iron rod of length 50 cm is joined at an end to aluminium rod of length 100 cm. All measurements refer to `20^(0) C` . Find the length of the composite system at `100^(o) C` and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminium are `12 X 10^(-6 ) C^(-1)` and `24 X10^(-6 ) C ^(-1)` respectively.

Text Solution

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Increase in length of combined rod = Increase in length of iron rod + Increase in length of copper rod
`(Delta1)=(Delta1)_(Fe)+(Delta1)_(Cu)`
`(1_(Fe)+1_(Cu))prop_("Avg")Deltat=1_(Fe)prop_(Fe)Deltat+1_(Cu)prop_(Cu)Deltat`
`prop_("Avg")=(1_(Fe)prop_(Fe)+1_(Cu)prop_(Cu))/((1_(Fe)+1_(Cu)))`
= `(50xx12xx10^(-6)+100xx17xx10^(-6))/150=15.33xx10^(-6)//""^(@)C`
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