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Home » A thin rod having length Lo at 0 degrees C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length. Answer: Consider the following diagram
A thin rod having length Lo at 0 degrees C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length. Answer: Consider the following diagram
CBSE | Class 11 | NCERT Exemplar | Physics | Thermal Properties of Matter
A thin rod having length Lo at 0 degrees C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length. Answer: Consider the following diagram

Answer:

Consider the following diagram:

From the diagram, this much can be said that:

\theta =\frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}

The temperature changes in a linear fashion from  θ1 to θ2. Let us assume that θ is the temperature at the rod’s middle. As a result, the average temperature at the rod’s midpoint is reported as:

L={{L}_{0}}(1+\alpha \theta )

L={{L}_{0}}\left[ 1+\alpha \left( \frac{{{\theta }_{1}}+{{\theta }_{2}}}{2} \right) \right]

i

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