Discussion
Consider the following statements :
1. The coefficient of linear expansion has dimension K-1.
2. The coefficient of volume expansion has dimension K-1.
Answer: A
Both 1 and 2 are correct.
The coefficient of linear expansion is \(\alpha = \frac{\Delta L}{L\,\Delta T}\) and the coefficient of volume expansion is \(\gamma = \frac{\Delta V}{V\,\Delta T}\). In each, a ratio of like quantities (length to length, volume to volume) is divided by a temperature change, so the dimension is \([K^{-1}]\), that is, per kelvin.
They differ in size (\(\gamma \approx 3\alpha\)) but not in dimension.
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