A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 17.7 m when the temperature is 21.2°C, what is the measured length when the temperature rises to 35.4°C? (Note: Do not neglect the expansion of the steel tape. Give your answer to three decimal places.)I am really confused... Could someone solve it for me with a step-by-step explanation? Thank you so much.
Assume linear thermal expansion with constant expansion coefficient. The change of length is given by: ΔL = L?·α·ΔT (L? initial length, α linear thermal expansion coefficient) The overall length of an object as function of temperature is: L= L? + ΔL = (1 + α·ΔT) · L? Consider the measurement at 21.2°C as reference: The aluminum column changes its length to L= (1 + α_aluminum · ΔT) · L? = (1 + 23×10-6 ^C°-1 · (35.4°C - 21.2°C) ) · 17.7m = 17.705m That would be the length measured with a steel tape at reference temperature of 21.2°C. Unfortunately the steel tape expands too. Because the scale increases with the expansion it measures too short. On the expanded tape you read the length L? while the actual length is L. Hence the measured length is: L? = L / (1 + α_steel · ΔT) = 17.705m / (1 + 11×10-6 ^C°-1 · (35.4°C - 21.2°C) ) = 17.003m
Aluminum cases offer better heat control than steel cases. Heat generating from the motherboard is absorbed by the case and then dissipated to the air. Aluminum dissipates heat better than steel. As for your question regarding ATX cases, have you tried using the barebone kits from Shuttle? Shuttle uses small form factor(i.e. small footprint). They are roughly the size of a shoe box.
