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physics ncert solutions class 11th Physics Class 11th Thermal Properties of Matter

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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Payal Gupta | Contributor-Level 10

5 months ago

11.10 Initial temperature, $T_{1}$ = 40.0°C, Final temperature, $T_{2}$ = 250°C, $?$ T = $T_{2}$ - $T_{1}$ = 210°C

Initial length of the brass rod at $T_{1}$ , $l_{b}$ = 50 cm, Initial diameter of the brass rod at $T_{1}$ , $d_{1}$ = 3 mm

Length of the steel rod $l_{s} = 50 c m$

For the expansion of the brass rod, we have:

$\frac{C h a n g e i n l e n g t h (? l_{b)}}{O r i g i n a l l e n g t h (l_{b)}}$ = $α_{b} ? T$ , then $? l_{b}$ = 50 $\times 2.0 \times 10^{- 5} \times 210$ = 0.21 cm

For the expansion of the steel rod, we have:

$\frac{C h a n g e i n l e n g t h (? l_{s)}}{O r i g i n a l l e n g t h (l_{s})}$ = $α_{b} ? T$ , then $? l_{s}$ = 50 $\times 1.2 \times 10^{- 5} \times 210$ = 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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