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\(^{-1}\)]
152.6 °C
182.6 °C
306.1 °C
335.5 °C
Correct answer is A
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