Question

Um bloco de ferro tem um volume de 50cm³ a 0°C. determine até qual temperatura devemos aquecê-lo a fim de que seu volume seja igual a 50,425cm³. Dado: coeficiente de dilatação linear do ferro = 12.10^-6 °C^-1.

Answer 1

T = 259.2 C

Step-by-step explanation:

In thermal expansion exercises, the equation is

ΔL = α L₀ ΔT

this equation is for one dimension, in the case of a volumetric body the equation changes to

ΔV = 3α V₀ ΔT

because the expansion is small

indicate that ΔV =V- V₀, the initial volume of V₀ = 50 cm³

ΔV = 0.425 cm³

ΔT = ΔV / (3α V₀)

ΔT = 0,425 / (50 3 12.1 10-6)

ΔT = 2,342 10² C

if we assume that initially the block is at room temperature To = 25C

the final temperature is

ΔT = T- To

T = ΔT + To

T = 234.2+ 25

T = 259.2 C