Question

a brass rod of length 40 cm and diameter 2 mm is joined to a steel rod of the same length and diameter at temperature 27 °C what is the change in length of the combined rod at 327 °C is given linear expansion for Steel is equal to 1.2 x 10 ^ 5 Kelvin inverse and linear expansion for brass is equal to 1.9 x 10 ^5 k inverse​

Answer 1

Answer:

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Answer 2

Answer:

Initial temperature, T1 =27°C

Final temperature, T2 = 327° C

Change in temperature, △T=T2 −T1= 300° C

Length of the brass rod at T1 ,l1 =40cm

Diameter of the brass rod at T1 ,d1 =0.3cm

Length of the steel rod at T2 ,l2 =40cm

Diameter of the steel rod at T2 ,d2=0.3mm

Coefficient of linear expansion of brass, α1 = 1.9×10^-5K^ −1

Coefficient of linear expansion of steel, α2 =1.2×10^−5K^−1

For the expansion in the brass rod, we have:

Change in length (△l1) / Original length (l1 )=α 1△T

∴△l1 =40×(1.9×10^−5)×300

=0.2280cm

For the expansion in the steel rod, we have:

Change in length (△l2 )/ Original length (l2 )=α2 △T

∴△l1 =40×(1.2×10^-5 )×300

=0.1440cm

Total change in the lengths of brass and steel,

△l=△l 1 +△l 2

=0.2280+0.1440

=0.3720cm

Total change in the length of the combined rod =0.3720cm

Since the rod expands freely from both ends, no thermal stress is developed at the junction.