A thin aluminum plate of area and thickness separates two large heat reservoirs

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

A thin aluminum plate of area

0.015\,\text{m}^2

and thickness

5.0\,\text{mm}

separates two large heat reservoirs. One side is held at

25\,^{\circ}\!\text{C}

and the other at

75\,^{\circ}\!\text{C}

. The thermal conductivity

k

of aluminum depends on temperature as shown: Temperature

\,(^{\circ}\!\text{C})

k

\,(\text{W}/(\text{m}\cdot\text{K}))

20 205 60 210 Assuming

k

varies linearly with temperature, estimate the total energy conducted through the plate in

2.0\,\text{min}

once steady state is reached.