11.10 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? Is there a ‘thermal stress’ developed at the junction ? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0 × 10–5 K–1, steel = 1.2 × 10–5 K–1 ).

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    11.10 Initial temperature, T1 = 40.0°C, Final temperature, T2 = 250°C, ? T = T2 - T1 = 210°C

    Initial length of the brass rod at T1 , lb = 50 cm, Initial diameter of the brass rod at T1 , d1 = 3 mm

    Length of the steel rod ls=50cm

    For the expansion of the brass rod, we have:

    Changeinlength(?lb)Originallength(lb) = αb?T , then ?lb = 50 ×2.0×10-5×210 = 0.21 cm

    For the expansion of the steel rod, we have:

    Changeinlength(?ls)Originallength(ls) = αb?T , then ?ls = 50 ×1.2×10-5×210 = 0.126 cm

    Total change in length = 0.21 + 0.126 = 0.336 cm

    Since the rods are free at the end, no thermal stress developed.

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