Answer:
[tex]1.8\times 10^{-5}/K[/tex]
Explanation:
Volume of glass flask,[tex]V_0=1000 cm^3[/tex]
[tex]T_1=1.00^{\circ} C[/tex]
[tex]T_2=52.0^{\circ} C[/tex]
Over flow[tex]\Delta V=8.25 cm^3[/tex]
Coefficient of mercury=[tex]\beta_{Hg}=18.0\times 10^{-5}/K[/tex]
[tex]\Delta V_{Hg}=\beta_{Hg}V_0(T_2-T_1)=18\times 10^{-5}\times 1000\times (52-1)[/tex]
[tex]\Delta V_{Hg}=9.18 cm^3[/tex]
[tex]\Delta_{gass}=\Delta V-\Delta_{Hg}=9.18-8.25=0.93 cm^3[/tex]
[tex]\beta_{gass}=\frac{\Delta V_{gass}}{V_0(T_2-T_1)}[/tex]
[tex]\beta_{gass}=\frac{0.93}{1000\times (52-1)}[/tex]
[tex]\beta_{gass}=1.8\times 10^{-5}/K[/tex]
Hence, the coefficient of volume expansion of the glass=[tex]1.8\times 10^{-5}/^{\circ} C[/tex]
The coefficient of volume expansion of the glass [tex]\bold { 1.8 x 10^-^5\ K^-^ 1}[/tex]
Given here,
Volume of the glass flask = 1000[tex]\bold {cm^3}[/tex]
Initial temperature = 1[tex]\bold{^oC}[/tex]
Final temperature = 52 [tex]\bold{^oC}[/tex]
[tex]\bold{ \Delta V = V_0 \beta \Delta T}[/tex]
Where,
[tex]\bold {\Delta V}[/tex] - Change in volume
[tex]\bold{V_0}[/tex] - initial volume = 1000cm
[tex]\bold {\beta }[/tex] - coefficient of volume expansion
[tex]\bold{\Delta T }[/tex] - temperature [tex]\bold { = T_2- T_1}[/tex]
Put the values in the formula
[tex]\bold {\Delta V_H_g = 18\times 10^-^5 \times 1000\times 51}\\\\\bold {\Delta V_H_g = 9.18 cm^3}[/tex]
[tex]\bold {\Delta Vglass = \Delta V_H_g - \Delta _H_g}\\\\\bold {\Delta Vglass = 9.18 -8.25 }\\\\\bold {\Delta Vglass = 0.93 cm^3}[/tex]
So, coefficient of volume expansion for gas,
[tex]\bold {\beta glass = \dfrac {0.93 }{1000 \times 51}}\\\\\bold {\beta glass = 1.8 x 10^-^5\ K^-^ 1}[/tex]
The coefficient of volume expansion of the glass [tex]\bold { 1.8 x 10^-^5\ K^-^ 1}[/tex]
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