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 ).
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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1 Answer
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11.10 Initial temperature, = 40.0°C, Final temperature, = 250°C, T = - = 210°C
Initial length of the brass rod at , = 50 cm, Initial diameter of the brass rod at , = 3 mm
Length of the steel rod
For the expansion of the brass rod, we have:
= , then = 50 = 0.21 cm
For the expansion of the steel rod, we have:
= , then = 50 = 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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