Along a copper wire running along the -axis

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Along a copper wire running along the xx-axis, the temperature at a distance xx cm from one end is given by T(x)=300+25e−0.1x  K.T(x)=300+25e^{-0.1x}\;\text{K}. The resistivity of copper at temperature TT Kelvin is ρ(T)=ρ0 [1+β (T−300)],\rho(T)=\rho_0\,[1+\beta\,(T-300)], where ρ0=1.7×10−8  Ω m\rho_0=1.7\times10^{-8}\;\Omega\,\text{m} and β=3.9×10−3  K−1\beta=3.9\times10^{-3}\;\text{K}^{-1}. (i) Find dTdx\dfrac{dT}{dx} at any point xx. (ii) Find an expression for dρdT\dfrac{d\rho}{dT}. (iii) Hence calculate dρdx\dfrac{d\rho}{dx} at x=5x=5 cm and state its units.

Related theory

Browse the problem library