(C) Let $h_1 = 120 \, cm$ be the height of the liquid at $0^{\circ}C$ (left tube).Let $h_2 = 120 + 4 = 124 \, cm$ be the height of the liquid at $30^{

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(C) Let $h_1 = 120 \, cm$ be the height of the liquid at $0^{\circ}C$ (left tube).Let $h_2 = 120 + 4 = 124 \, cm$ be the height of the liquid at $30^{\circ}C$ (right tube).Since the pressure at the bottom of both tubes must be equal:$h_1 \rho_1 g = h_2 \rho_2 g$$\rho_1 h_1 = \rho_2 h_2$Since $\rho_2 = \frac{\rho_1}{1 + \gamma \Delta T}$,where $\Delta T = 30^{\circ}C - 0^{\circ}C = 30^{\circ}C$:$h_1 = h_2 \left( \frac{1}{1 + \gamma \Delta T} \right)$$1 + \gamma \Delta T = \frac{h_2}{h_1} = \frac{124}{120}$$\gamma \Delta T = \frac{124}{120} - 1 = \frac{4}{120} = \frac{1}{30}$$\gamma = \frac{1}{30 \times 30} = \frac{1}{900} \approx 0.00111 \, /^{\circ}C$$\gamma \approx 11.11 \times 10^{-4} /^{\circ}C$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Thermal Expansion for fluid

Two vertical glass tubes filled with a liquid are connected by a capillary tube as shown in the figure. The tube on the left is put in an ice bath at $0^{\circ}C$ while the tube on the right is kept at $30^{\circ}C$ in a water bath. The difference in the levels of the liquid in the two tubes is $4 \, cm$ while the height of the liquid column at $0^{\circ}C$ is $120 \, cm$. The coefficient of volume expansion of the liquid is (Ignore expansion of the glass tube):

A
$22 \times 10^{-4}/^{\circ}C$
B
$1.1 \times 10^{-4}/^{\circ}C$
C
$11 \times 10^{-4}/^{\circ}C$
D
$2.2 \times 10^{-4}/^{\circ}C$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Thermal Expansion for fluid

The densities of a liquid at $0^{\circ} C$ and $100^{\circ} C$ are respectively $1.0127 \ g/cm^3$ and $1 \ g/cm^3$. $A$ specific gravity bottle is filled with $300 \ g$ of the liquid at $0^{\circ} C$ up to the brim and it is heated to $100^{\circ} C$. Then,the mass of the liquid expelled in grams is: (Coefficient of linear expansion of glass $= 9 \times 10^{-6} /^{\circ} C$)

DifficultTS EAMCET 2003

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The coefficient of linear expansion of a vessel completely filled with $Hg$ is $1 \times 10^{-5} /^{\circ} C$. If there is no overflow of $Hg$ on heating the vessel,then the coefficient of cubical expansion of $Hg$ is:

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$A$ glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over,if the coefficient of linear expansion of glass is $\alpha_g$ and the coefficient of volume expansion of the liquid is $\gamma_L$?

MediumAP EAMCET 2021

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$A$ glass flask is filled up to a mark with $50\, cc$ of mercury at $18^{\circ}C.$ If the flask and contents are heated to $38^{\circ}C,$ how much mercury will be above the mark? (Given: $\alpha$ for glass is $9 \times 10^{-6} {^{\circ}C}^{-1}$ and the coefficient of real expansion of mercury is $180 \times 10^{-6} {^{\circ}C}^{-1}$)

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The coefficient of apparent expansion of a liquid in a copper vessel is $C$ and in a silver vessel is $S$. The coefficient of volume expansion of copper is $\gamma_c$. What is the coefficient of linear expansion of silver?

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The coefficient of linear expansion of a vessel completely filled with $Hg$ is $1 \times 10^{-5} /^{\circ} C$. If there is no overflow of $Hg$ on heating the vessel,then the coefficient of cubical expansion of $Hg$ is:

$A$ glass vessel of volume $V_0$ is completely filled with a liquid and its temperature is raised by $\Delta T$. What volume of the liquid will flow over,if the coefficient of linear expansion of glass is $\alpha_g$ and the coefficient of volume expansion of the liquid is $\gamma_L$?

The coefficient of apparent expansion of a liquid in a copper vessel is $C$ and in a silver vessel is $S$. The coefficient of volume expansion of copper is $\gamma_c$. What is the coefficient of linear expansion of silver?

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