Heat and Thermodynamics 2 Question 2

5. A pendulum clock loses 12s a day if the temperature is 40C and gains 4s a day if the temperature is 20C. The temperature at which the clock will show correct time, and the coefficient of linear expansion α of the metal of the pendulum shaft are, respectively.

(2016 Main)

(a) 25C,α=1.85×105/C

(b) 60C,α=1.85×104/C

(c) 30C,α=1.85×103/C

(d) 55C,α=1.85×102/C

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Answer:

Correct Answer: 5. (a)

Solution:

T0=2πLgT=T0+ΔT=2πL+ΔLgT=T0+ΔT=2πL(1+αΔθ)g=2πLg(1+αΔθ)12T0(1+αΔθ2)ΔT=TT0=αΔθT02 or ΔT1ΔT2=αΔθ1T0αθ2T0124=40θθ203(θ20)=40θ4θ=100θ=25C

Time gained or lost is given by

ΔT=(ΔTT0+ΔT)tΔtT0t

From Eq. (i), ΔTT0=αΔθ2

Δt=α(Δθ)t212=α(4025)(24×3600)2α=1.85×105/C



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