Question

A brass rod of length 50 cm and diameter 3 mm is joined to a steel rod of same length and same diameter find the change in length of combined rod at 250 degree celsius if the original length have been measured at 40 degree celsius is there a thermal stress developed at the junction when the ends of rod are free to expand

Answer 1

No thermal stress do not develop at the junction. Because the rod expand freely hence no thermal stress is developed.

Answer 2

Answer:

0.336 cm

Explanation:

Here,

intial temperature ( T1) = 40°C

Final temperature ( T2) = 250°C

so, increase in temperature (∆T) = 250 - 40 =210°C

For brass rod,

Intial length ( Lo) = 50 cm

Let Final length = L

Coefficient of linear expansion (a) = 2 × 10^-5 /°C

L = Lo(1 + a∆T)

= 50( 1 + 2 × 10^-5 × 210)

=50( 1 + 420 × 10^-5)

= 50× 1.00420

= 50.21 cm

Increase in length ( ∆L) = L2 - L1

= 50.21 - 50

= 0.21 cm

For steel rod,

Intial length ( Lo') = 50 cm

Coefficient of linear expansion ( a') = 1.2 × 10^-5/K

Final length ( L') = Lo'(1 + a'∆T)

= 50( 1 + 1.2 × 10^-5 × 210)

= 50 × 1.00252

= 50.126 cm

Increase in length ( ∆L') = 50.126 cm - 50 cm = 0.126 cm

Total inches in length = ∆L + ∆L'

= 0.21 + 0.126

= 0.336 cm