Question

Consider the following statements.
(A) The coefficient of linear expansion has dimension $K^{-1}$
(B) The coefficient of volume expansion has dimension $K^{-1}$

• A. Both A and B are correct
• B. A is correct but B is wrong
• C. B is a correct but A is wrong
• D. Both A and B are wrong

Answer 1

Answer: (A)

Both A and B are correct

The coefficient of linear expansion is given by:

$\alpha =\frac{\Delta l}{l\times \Delta t}$

where, $l=1m\left(let\right)=$ initial length of rod

$\Delta l=1m\left(let\right)=$ change in length of rod

$\Delta t=1K\left(let\right)=$ change in temperature

Now, $\alpha =\frac{1m}{1m\times 1K}=1K^{-1}$

Similarly, the coefficient of volume expansion is given by:

$\gamma =\frac{\Delta V}{V\times \Delta t}$

where, $V=1m^3\left(let\right)=$ initial volume

$\Delta V=1m^3\left(let\right)=$ change in volume

$\Delta t=1K\left(let\right)=$ change in temperature

Now, $\gamma =\frac{1m^3}{1m^3\times 1K}=1K^{-1}$

Hence both $\alpha$ and $\gamma$ have the dimension $K^{-1}$.