The length of an object varies with temperature according to L = -5T + 3T³ The coefficient of linear expansion of this object is A) (-5 + 9T²)/L B) -5/L C) (-5 + 6T²)/L D) 9T² E) 9T²/L

Question

Quizplus · Accepted Answer

The coefficient of linear expansion (α) is defined as the fractional increase in length per unit increase in temperature. Mathematically, α = (ΔL/L)/(ΔT/T). Using the given equation for length, we can find the fractional increase in length as ΔL/L = -5/3. Substituting this and simplifying, we get: α = (-5/3)/(ΔT/T) = (-5/3)*(T/ΔT) Now, using the chain rule of differentiation, we can write: ΔL/L = (∂L/∂T)*(ΔT/T) Or, -5/3 = (-5 + 3³T)/L * (ΔT/T) Equating coefficients and simplifying, we get: ΔT/T = 9/(-5 + 3³T) = 9T²/L Thus, α = (ΔL/L)/(ΔT/T) = (-5/3)/(9T²/L) = (-5 + 9T²)/L, which is the answer choice A.

The Length of an Object Varies with Temperature According to