The diameter of a brass ring at 30 °C is 50.0 cm. To what temperature must this ring be heated to increase its diameter to 50.29 cm? [ linear expansivity of brass = 1.9 x 10\(^{-5}\) K\(^{-1}\)]

  • A 152.6 °C
  • B 182.6 °C
  • C 306.1 °C
  • D 335.5 °C
waec 2022physics

The correct answer is A. 152.6 °C

L1=50.

T1 = 30 + 273 = 303k

Linear expansivity =  1.9 x 10\(^{-5}\)

L2 = 50.29

Temp rise= ?

L2 - L1 = 50.29 - 50 = 0.29

Linear expansivity = \(\frac{L2-L1}{L1(T2-T1)}\)

1.9 x 10\(^{-5}\) = \(\frac{0.29}{50*(T2 - 303)}\)

1.9 x 10\(^{-5}\) * 50 (T2 - 303) = 0.29

T2 = \(\frac{0.29}{50 * 1.9 * 10^{-5}}\) + 303

T2 = 152.6 °C

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