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

An iron rod of length 50cm is joined at an end to copper rod of length 100cm at `20^(@)C`. Find the length of the system at `100^(@)C` and average coefficient of linear expansion of the system.
`(alpha_("iron")=12xx10^(-6)//""^(@)Candalpha_("copper")=17xx10^(-6)//""^(@)C.)`

Text Solution

Verified by Experts

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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