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  4. The coefficients of linear expansion of P and Q are α1 and α2 respectively. If the coefficient of cubical expansion of 'Q' is three times the coefficient of superficial expansion of P, then which of the following is true?

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Q. The coefficients of linear expansion of P and Q are $\alpha_1$ and $\alpha_2$ respectively. If the coefficient of cubical expansion of 'Q' is three times the coefficient of superficial expansion of P, then which of the following is true?

Thermal Properties of Matter

Solution:

First we note that coefficient of cubical expansion $=3 x$ coefficient of linear expansion
Coefficient of superficial expansion $=2 x$ coefficient of linear expansion Now it is given that coefficient of cubical expansion of $Q$ is three times the coefficient of superficial expansion of P.
So, $3 \times$ coefficient of linear expansion of $Q=3 \times 2 \times$ coefficient of linear expansion of $P$
So $\alpha_{2}=2 \times \alpha_{1}$