The two ends of a rod of length $\mathrm{L}$ and a uniform cross-sectional area A are kept at two…

The two ends of a rod of length $\mathrm{L}$ and a uniform cross-sectional area A are kept at two temperatures $T_1$ and $T_2\left(T_1 > T_2\right)$. The rate of heat transfer, $\frac{\mathrm{dQ}}{\mathrm{dt}}$, through the rod in a steady state is given by :
  1. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{kA}\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{L}}$
  2. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{kL}\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{A}}$
  3. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{k}\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{LA}}$
  4. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{kLA}\left(\mathrm{T}_1-\mathrm{T}_2\right)$

Solution

For steady state $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{kA}\left(\mathrm{T}_1-\mathrm{T}_2\right)}{\mathrm{L}}$ .

Asked in: NEET 2009 (Mains)

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