Question

If the coefficient of linear expansion of glass is $0.000009$, the coefficient of cubical expansion of glass is:

& A.0.0000027 \\\ & B.0.000027 \\\ & C.0.00027 \\\ & D.0.000018 \\\ \end{aligned}$$

Answer 1

To begin with, we can define what is linear expansion and cubical expansion, then we can identify the coefficient of the two and compare them to find the required answer. Since one factor i.e. the coefficient of linear expansion of glass is given in the question, we can find the other.
Formula used:
$\alpha_{V}=3\times \alpha_{L}$

Complete answer:
We know that expansion means a change in volume or length, more specifically increase in volume or length. This is majorly due to increase in pressure. Thus, we can say that linear expansion is the change in volume due to change in length majorly due some temperature, at constant pressure. Thus, the coefficient of linear expansion $\alpha_{L}$, is the rate at which length $d\;L$ changes with respect to temperature $d\;T$. Mathematically, it is given as $\alpha_{L}=\dfrac{dL}{dT}$
Similarly, cubic expansion is the change in volume due some temperature at a constant pressure. Thus, the coefficient of cubic expansion $\alpha_{V}$, is the rate at which length $d\;V$ changes with respect to temperature $d\;T$. Mathematically, it is given as $\alpha_{V}=\dfrac{dV}{dT}$
Also, $\alpha_{V}=3\times \alpha_{L}$
Here, given that, $\alpha_{L}=0.000009$for glass, at some pressure. Then let $\alpha_{V}$ be the cubical coefficient at the same pressure, then substituting the value, we get, $\alpha_{V}=3\times 0.000009= 0.000027$.

So, the correct answer is “Option B”.

Note:
Coefficient of thermal expansions is the intrinsic property of the material. This is due to the cohesive forces between the molecules of the material. The SI units of the coefficient of expansions is $C^{-1}$ and $K^{-1}$. Both linear and cubic coefficients are under the category of thermal expansion with some variation. Also note that the this value is applicable only at constant pressure