A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250^(@)C, if the original lengths are at 40.0^(@)C ? there a 'thermal stress' developed at the junction ? The ends of the rod are free to expand (Coefficient of linear expansion of brass =2.0xx10^(-5)K^(-1)," steel "=1.2xx10^(-5)K^(-1)).

A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel r

1.	A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250^(@)C, if the original lengths are at 40.0^(@)C ? there a 'thermal stress' developed at the junction ? The ends of the rod are free to expand (Coefficient of linear expansion of brass =2.0xx10^(-5)K^(-1)," steel "=1.2xx10^(-5)K^(-1)).
Answer» Solution :Increase in length of brass rod, `Deltal_(1)=alpha_(1)l_(1)DeltaT""[becausel_(1)=50" CM",DeltaT=250-40=210^(@)C]` `=2xx10^(-5)xx50xx210` `=420xx50xx10^(-5)` `=0.21` cm Increase in length of steel rod, `Deltal_(2)=alpha_(2)l_(2)DeltaT[becausel_(2)=50" cm"]` `=1.2xx10^(-5)xx50xx210` `=0.126` cm TOTAL increase in combined rod, `DELTAL=Deltal_(1)+Deltal_(2)` `=0.21+0.126` `=0.336`cm `~~0.34` cm No, thermal stress is not DEVELOPED at the junction as rods are not clamped at end.