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An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)
- a)50.7℃
- b)69.0℃
- c)143.7℃
- d)33.7℃
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
An aluminum bar of 8 m length and a steel bar of 5 mm longer in lengt...
L = 8 m Initially,
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αs = 12 x 10−6/℃
αa = 23 x 10−6/℃
t1 = 30℃
Total elongation of aluminum-total elongation of steel
= (AA3) − (A1A2)
= (AA1) + A1A2 + A2A3) − (A1A2)
= AA1 + A2A3 = 10mm
L αal∆t − Lαs∆t = 10
8 x 103 x ∆t[23 x 10−6 − 12 x 10−6] = 10
t2 − 30° = 113.636℃
t2 = 143.636℃
Most Upvoted Answer
An aluminum bar of 8 m length and a steel bar of 5 mm longer in lengt...
Solution:
Given data:
Length of Aluminum bar, L_Al = 8 m
Length of Steel bar, L_St = L_Al + 5 mm
The initial temperature of both bars, T = 30℃
Linear expansion coefficient of Steel, α_St = 12 x 10^-6/℃
Linear expansion coefficient of Aluminum, α_Al = 23 x 10^-6/℃
Let's assume that at temperature T1, the length of the steel bar increases by 5 mm than the aluminum bar.
The change in length of the Steel bar, ΔL_St = L_Stα_St(T1 - T)
The change in length of the Aluminum bar, ΔL_Al = L_Alα_Al(T1 - T)
ΔL_St - ΔL_Al = 5 mm
Putting the values, we get:
(L_Stα_St - L_Alα_Al)(T1 - T) = 5 mm
(8.005 x 10^-3 x 12 x 10^-6/℃ - 8 x 10^0 x 23 x 10^-6/℃)(T1 - 30℃) = 5 x 10^-3 m
T1 - 30℃ = 143.7℃
Therefore, the temperature at which the Aluminum bar will elongate 5 mm longer than the Steel bar is:
T1 = 143.7℃
Hence, the correct answer is option 'C'.
Given data:
Length of Aluminum bar, L_Al = 8 m
Length of Steel bar, L_St = L_Al + 5 mm
The initial temperature of both bars, T = 30℃
Linear expansion coefficient of Steel, α_St = 12 x 10^-6/℃
Linear expansion coefficient of Aluminum, α_Al = 23 x 10^-6/℃
Let's assume that at temperature T1, the length of the steel bar increases by 5 mm than the aluminum bar.
The change in length of the Steel bar, ΔL_St = L_Stα_St(T1 - T)
The change in length of the Aluminum bar, ΔL_Al = L_Alα_Al(T1 - T)
ΔL_St - ΔL_Al = 5 mm
Putting the values, we get:
(L_Stα_St - L_Alα_Al)(T1 - T) = 5 mm
(8.005 x 10^-3 x 12 x 10^-6/℃ - 8 x 10^0 x 23 x 10^-6/℃)(T1 - 30℃) = 5 x 10^-3 m
T1 - 30℃ = 143.7℃
Therefore, the temperature at which the Aluminum bar will elongate 5 mm longer than the Steel bar is:
T1 = 143.7℃
Hence, the correct answer is option 'C'.
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An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer?
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An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer?.
An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum bar of 8 m length and a steel bar of 5 mm longer in length are kept at 30℃.If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5 mm longer than the steel bar? (The linear expansion coefficients for steel and aluminum are 12 x 10−6/℃ and 23 x 10−6/℃ respectively)a) 50.7℃b) 69.0℃c) 143.7℃d) 33.7℃Correct answer is option 'C'. Can you explain this answer?.
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