Question

If $\gamma $ (apparent) of a liquid in a vessel is $76\% $ of $\gamma $(real) of that liquid, the coefficient of linear expansion of the vessel is
(A) $80\% \,of\gamma $ (Real)
(B) $16\% \,of\gamma $ (Real)
(C) $24\% \,of\gamma $ (Real)
(D) $24\% \,of\gamma $ (Real)

Answer 1

Hint:In this question, first consider the expression for the coefficient of apparent expansion. Substitute the required values in the obtained expression to determine the value of the coefficient of linear expansion of the vessel. The value of the coefficient of linear expansion of the vessel should be in percentage. Therefore, multiply the decimal value by 100 to get the value in percentage.

Complete Step by Step Solution:
In this question, we have given the coefficient of apparent expansion in the liquid in a vessel is $\gamma = 76\% $ of real value.
As we know that the general expression for the coefficient of apparent expansion is a numerical term that shows the fraction of volume increase or decrease during the heat transfer process.
When any object absorbs or rejects the heat, its volume changes a numerical term that shows the fraction of volume increase or decrease during the heat transfer process is terms as the coefficient of apparent expansion.
We can write the mathematical expression for the coefficient of apparent as given below.
\[ \Rightarrow a = \gamma r - \gamma g\]
Now we substitute the values in the above expression.
\[ \Rightarrow \dfrac{{76}}{{100}}\gamma {\text{r}} = \gamma {\text{r}} - \gamma g\]
Now we simplify the above expression.
\[ \Rightarrow \dfrac{{24}}{{100}}\gamma {\text{r}} = \gamma {\text{g}}\]
Further solve the expression for $\left( {\alpha g} \right)$ we get,
\[\alpha {\text{g}} = \dfrac{1}{3} \times \dfrac{{24}}{{100}}\gamma {\text{r}}\]
We solve the expression to get value in the form of percentage.
\[ \Rightarrow \alpha g = 0.0{\text{8}} \times \gamma {\text{r}}\]
$\therefore 80\% \,of\gamma $ (Real).

Therefore, the option A is correct

Note: The final answer of the coefficient of linear expansion of the vessel is in percentage but the calculated value from the expression of the coefficient of apparent expansion is in decimal. So do not forget to convert the decimal value into the percentage.