A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume…

A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)
  1. $15.6 \times 10^{-4 \circ} \mathrm{C}^{-1}$
  2. $156 \times 10^{-4 \circ} \mathrm{C}^{-1}$
  3. $1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
  4. $0.156 \times 10^{4 \circ} \mathrm{C}^{-1}$

Solution

Coefficient of real expansion $\begin{aligned} & \gamma_R=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)} \\ & \text { Here, } \quad V_2=\frac{3}{4}, V_1=\frac{2}{3} \\ & \text { and } \quad\left(t_2-t_1\right)=(100-20)=80^{\circ} \mathrm{C} \\ & \therefore \quad \gamma_R=\frac{\left(\frac{3}{4}-\frac{2}{3}\right)}{\frac{2}{3}(80)}=\frac{1}{640} \\ & =15.6 \times 10^{-4} \circ \mathrm{C}^{-1} \\ & \end{aligned}$

Asked in: AP EAMCET 2011

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