Heat and Thermodynamics 2 Question 5

8. A bimetallic strip is formed out of two identical strips-one of copper and the other of brass. The coefficients of linear expansion of the two metals are αC and αB. On heating, the temperature of the strip goes up by ΔT and the strip bends to form an arc of radius of curvature R. Then, R is (1999,3M)

(a) proportional to ΔT

(b) inversely proportional to ΔT

(c) proportional to |αBαC|

(d) inversely proportional to |αBαC|

Integer Answer Type Question

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Answer:

Correct Answer: 8. 6.7×105/C

Solution:

  1. Let l0 be the initial length of each strip before heating. Length after heating will be

lB=l0(1+αBΔT)=(R+d)θlC=l0(1+αCΔT)=Rθ

[From binomial expansion]

R=d(αBαC)ΔT or R1ΔT1|αBαC|



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