Given αsteel = 1.20 x 10-5 K-1 (coefficient of lin. exp. of steel)
T1 = 27°C = 27 + 273 K = 300 K
Length at temperature, T1K = lT1 = 8.70 cm
Length at temperature, T2K = lT2 = 8.69 cm
Change in length = lT2 - lT1 = lT1 α(T2 - T1)
⇒ 8.69 - 8.70 = 8.70 x (1.20 x 10-5) x (T2 - 300)
⇒ T2 - 300 = {0.01}/{8.70 x 1.2 x 105} = -95.8
T2 = 300 - 95.8 = 204.2 K
= -68.8°C