The two ends of a rod of length L and a uniform cross-sectional area A are kept at two temperatures T_1 and T_2(~T_1>T_2) . The rate of heat transfer, dQ dt , through the rod in a steady state is given by

NEET 2009

NEET 2009 · Physics · Thermal Properties of Matter

The two ends of a rod of length L and a uniform cross-sectional...

The two ends of a rod of length

L

and a uniform cross-sectional area

A

are kept at two temperatures

\mathrm{T}_1

and

\mathrm{T}_2\left(\mathrm{~T}_1>\mathrm{T}_2\right)

. The rate of heat transfer,

\frac{\mathrm{dQ}}{\mathrm{dt}}

, through the rod in a steady state is given by

A\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL} $\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{A}}$
B\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K} $\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{LA}}$
C $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{KLA}\left(\mathrm{T}_1-\mathrm{T}_2\right)$
D\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA} $\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{L}}$

D. \frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA} $\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{L}}$

For a rod of length

L and area of cross-section

whose faces are maintained at temperature

\mathrm{T}_1

and

\mathrm{T}_2

respectively. Then in steady state the rate of heat flowing from one face to the other face in time

is given by

\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}

\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{L}}

The curved surface of rod is kept insulated from surrounding to avoid leakage of heat.