Question

Hello, please help me to resolve the following problem which answer is 43 degrees Celsius. I just need you to show me how to get to that result. Please provide detailed explanation of the procedures used to resolve it. This problem was submitted previously, but the person who tried got the wrong answer.

At 175 °C, a brass plate completely fills a frame which has dimensions 2.38 m by 1.67 m. Ignoring the thermal expansion of the frame, to what temperature would the brass plate need to be cooled so that it only fills 99.5% area of the frame? 2.38 m brass plate in the frame at 475 °C 1.6 m for brass, a = 19.0x10-6 °C-1

Answer 1

Here Area A, at temp. Ti =175°C is givenas I A1 = 2.38×1.67 = 3.9746 m² Now it area at oc is to the - At='Ao + A. (201) * T OY Aos_ it 22 T or A =- 3.9746 -= 3.94834 m² 1+ 2x19x106x175 5% of area A, is Az then A₂ = 0.9958A =0.9958 3.9746=3.954727m² Now it temp. is Tz for area A2 then Az = Ac +A(2x) Tz or T2 = A - Ao 3.954727-3.94834 " =42.68 _ A0 (22) = 3.94834 X2X19X156 or T2 = 43°C