One-dimensional steady state heat conduction takes place through a sol...
Explanation:
In one-dimensional steady state heat conduction, the temperature distribution in the solid depends on the variation of cross-sectional area in the direction of heat transfer. Let's analyze each option to understand which one is correct.
Option A: Quadratic
A quadratic temperature distribution would imply that the temperature varies with the square of the distance. However, since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, a quadratic temperature distribution is not possible in this case.
Option B: Exponential
An exponential temperature distribution would imply that the temperature varies exponentially with the distance. However, since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, an exponential temperature distribution is not possible in this case.
Option C: Logarithmic
A logarithmic temperature distribution would imply that the temperature varies logarithmically with the distance. In this case, as the cross-sectional area varies linearly, the distance is also varying linearly. Therefore, a logarithmic temperature distribution is possible in this case.
Option D: Linear
A linear temperature distribution would imply that the temperature varies linearly with the distance. Since the cross-sectional area varies linearly, this means that the distance is also varying linearly. Therefore, a linear temperature distribution is possible in this case.
Conclusion:
The correct answer is option C: Logarithmic. The temperature distribution in the solid will follow a logarithmic variation with the distance due to the linear variation of the cross-sectional area in the direction of heat transfer.