Sl.no | l (m) | ∆T (oC) | ∆l (m) |
1 | 2 | 10 | 4 × 10-4 |
2 | 1 | 10 | 4 × 10-4 |
3 | 2 | 20 | 2 × 10-4 |
4 | 3 | 10 | 6 × 10-4 |
If the first observation is correct, what can you say about observations 2, 3, and 4.
Answer:
Assume that the first observation is right, which indicates that the linear expansion coefficient is as follows:
$ \alpha =\frac{\Delta l}{l\times \Delta T}=\frac{4\times {{10}^{-4}}}{2\times 10} $
$ \alpha =2\times {{10}^{-5}}{{C}^{-1}} $
For second observation,
$ \Delta l=\alpha l\Delta T=2\times {{10}^{-4}}m\ne 4\times {{10}^{-4}}m $
which is incorrect. For third observation, we have –
$ \Delta l=\alpha l\Delta T=8\times {{10}^{-4}}m\ne 2\times {{10}^{-4}}m $
Which is incorrect. Now, for fourth observation, we have –
$ \Delta l=\alpha l\Delta T=6\times {{10}^{-4}}m=6\times {{10}^{-4}}m $
which is correct.