Question

When a liquid, filled in two vessels A and B of equal volumes, is heated, the coefficients of apparent expansions of the liquids are formed to be ${\gamma }_1$ and ${\gamma }_2$ respectively. If ${\alpha }_1$ be the coefficient of linear expansion of A, then the coefficient of linear expansion of B will be:

• A. $\frac{{\gamma }_2-{\gamma }_1}{3}+{\alpha }_1$
• B. $\frac{{\gamma }_2-{\gamma }_1}{3}-{\alpha }_1$
• C. $\frac{{\gamma }_1-{\gamma }_2}{3}+{\alpha }_1$
• D. $\frac{{\gamma }_1-{\gamma }_2}{3}-{\alpha }_1$

Answer 1

The correct option is A $\frac{{\gamma }_2-{\gamma }_1}{3}+{\alpha }_1$

Let the actual coefficients of volume expansion be ${\gamma }_1^{\prime }$ and ${\gamma }_2^{\prime }$. Then,

${\gamma }_1^{\prime }={\gamma }_1-{\gamma }_{vessel}$ and ${\gamma }_2^{\prime }={\gamma }_2-{\gamma }_{vessel}$

${\gamma }_2^{\prime }-{\gamma }_1^{\prime }={\gamma }_2-{\gamma }_1$.........................$\left(i\right)$

Since, Linear expansion ${\alpha }_1^{\prime }=\frac{{\gamma }_1^{\prime }}{3}$

${\alpha }_2=\frac{{{\gamma }^{\prime }}_2}{3}-{\alpha }_1^{\prime }+{\alpha }_1=\frac{{\gamma }_2^{\prime }-{{\gamma }^{\prime }}_1}{3}+{\alpha }_1=\frac{{\gamma }_2-{\gamma }_1}{3}+{\alpha }_1$