Question

[8 points] By using the heat equation, find the temperature $u(x, t)$ in a bar of silver of length 1.0 cm and constant cross section of area 1.0 cm$^2$ (density 1.0 g/cm$^3$, thermal conductivity 1.0 cal/(cm sec $^\circ$C), specific heat 1.0 cal/(g $^\circ$C)) that is perfectly insulated \"laterally\", with ends kept at temperature 0$^\circ$C and initial temperature $f(x)$ $^\circ$C, where $f(x) = \sin \pi x + \sin 5\pi x$ (7)

          [8 points] By using the heat equation, find the temperature $u(x, t)$ in a bar of silver of length 1.0 cm and constant cross section of area 1.0 cm$^2$ (density 1.0 g/cm$^3$, thermal conductivity 1.0 cal/(cm sec $^\circ$C), specific heat 1.0 cal/(g $^\circ$C)) that is perfectly insulated \"laterally\", with ends kept at temperature 0$^\circ$C and initial temperature $f(x)$ $^\circ$C, where

$f(x) = \sin \pi x + \sin 5\pi x$
(7)

[8 points] By using the heat equation, find the temperature u(x, t) in a bar of silver of length 1.0 cm and constant cross section of area 1.0 cm^2 (density 1.0 g/cm^3, thermal conductivity 1.0 cal/(cm sec ^∘C), specific heat 1.0 cal/(g ^∘C)) that is perfectly insulated l̈aterally,̈ with ends kept at temperature 0^∘C and initial temperature f(x) ^∘C, where

f(x) = sinπ x + sin 5π x
(7)

Added by Tiffany H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Manik Pulyani

02/06/2022

Step 1

Step 1: The heat equation is given by: $$\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}$$ where $k$ is the thermal diffusivity. Show more…

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[8 points] By using the heat equation, find the temperature u(x,t) in a bar of silver of length 1.0 cm and constant cross section of area 1.0 cm² (density 1.0 g/cm³, thermal conductivity 1.0 cal/(cm sec°C), specific heat 1.0 cal/(g°C)) that is perfectly insulated "laterally", with ends kept at temperature 0°C and initial temperature f(x) °C, where $$f(x) = sin \pi x + sin 5\pi x$$ (7)