A steel rod of length and cross-sectional area connects a furnace maintained at to a…

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A steel rod of length

0.25\,\text{m}

and cross-sectional area

2.0\times10^{-4}\,\text{m}^2

connects a furnace maintained at

400^{\circ}\text{C}

to a

1.0\,\text{kg}

copper block that is initially at

25^{\circ}\text{C}

. The surroundings are well insulated so that all energy conducted through the rod raises the block’s temperature. Treat the temperature difference between the furnace and the block as constant at

370\,\text{K}

during the heating interval. How much time is required for the block to reach

55^{\circ}\text{C}

? (Thermal conductivity of steel:

k=50\,\text{W}/\text{m}\cdot\text{K}

; specific heat of copper:

c=390\,\text{J}/\text{kg}\cdot\text{K}

.) (a)

7.9\times10^{1}\,\text{s}

(b)

3.2\times10^{3}\,\text{s}

(c)

7.9\times10^{2}\,\text{s}

(d)

9.9\times10^{3}\,\text{s}

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