Q. 103.5( 12 Votes )

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).

Answer :

Given,

Initial temperature, T1 = 40°C = 40 + 273.15 K = 313.15K


Final temperature, T2 = 250°C = 250 + 273.15 = 523.15 K


Length of the brass rod at T1, L1 = 50 cm = 0.5 m


Diameter of the brass rod at T1, d1 = 3.0 mm = 3 × 10-3 m


Length of the steel rod at T2, L2 = 50 cm = 0.5 m


Diameter of the steel rod at T2, d2 = 3.0 mm = 3 × 10-3 m


Coefficient of linear expansion of brass, α1 = 2.0 × 10–5 K–1 Coefficient of linear expansion of steel, α2 = 1.2 × 10–5 K–1


Change in temperature, ΔT = T2 – T1 = 523.15 K-313.15K=210 K


For the expansion in the brass rod,


Change in length (∆L1)/Original length (L1) = α1ΔT


ΔL1 = α1L1ΔT


ΔL1 = (2.0 × 10–5 K–1)×(0.5 m)×(210 K)


ΔL1 = 0.0021 m = 0.21 cm


For the expansion in the steel rod,


Change in length (∆L2)/Original length (L2) = α2ΔT


∆L2 = α2L2ΔT


∆L2 = (1.2 × 10–5 K–1)×(0.5 m)×(210 K)


∆L2 = 0.00126 m = 0.126 cm


Total change in length, ΔL = ∆L1 + ∆L2


ΔL = 0.21 cm + 0.126 cm


∆L= 0.336 cm


No thermal stress develops at the junction since both the ends of the rod expand freely.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Thermal Properties of Matter | Matering important conceptsThermal Properties of Matter | Matering important conceptsThermal Properties of Matter | Matering important concepts48 mins
Laws of states of matterLaws of states of matterLaws of states of matter44 mins
Interactive quiz on liquefactionInteractive quiz on liquefactionInteractive quiz on liquefaction44 mins
Liquefaction of gasesLiquefaction of gasesLiquefaction of gases53 mins
Gaseous state- interactive quizGaseous state- interactive quizGaseous state- interactive quiz56 mins
Interactive quiz on Kinetic Theory and Real Gas equationInteractive quiz on Kinetic Theory and Real Gas equationInteractive quiz on Kinetic Theory and Real Gas equation52 mins
Interactive quiz on Measurement of Pressure & Dalton's Law.Interactive quiz on Measurement of Pressure & Dalton's Law.Interactive quiz on Measurement of Pressure & Dalton's Law.49 mins
Fluid StaticsFluid StaticsFluid Statics67 mins
Learn About Bernoulli's TheoremLearn About Bernoulli's TheoremLearn About Bernoulli's Theorem45 mins
Measurement of Pressure & Dalton's Law.Measurement of Pressure & Dalton's Law.Measurement of Pressure & Dalton's Law.64 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :