Respuesta :
Answer: the coefficient of volume expansion of glass = 0.86/(1000 * 52) = 0.00001654 per degree.
Explanation:
Original volume of mercury = 1000 cm3.
The final volume of mercury considering its volume expansion quotient = 1000 + 1000*(1.8*10^-4 *52) = 1000 + 9.36 = 1009.36 cm^3
Considering the glass as a non expanding substance, the complete excess volume of 9.36 cm3 of mercury should have overflown the container, but due to the expansion of glass, the capacity of mercury containment increases and so a lesser amount of mercury flows out.
The amount of mercury that actually flowed out = 8.50 cm3.
So, the expansion of the glass container = 9.36-8.50 = 0.86 cm3.
Using the formula for coefficient of expansion,
coefficient of volume expansion of glass = 0.86/(1000 * 52) = 0.00001654 per degree.
The coefficient of expansion for glass has been calculated as 1.8 [tex]\rm \times\;10^-^5\;K^-^1[/tex].
The coefficient of volume expansion has been the change in volume due to the thermal expansion.
The coefficient of volume expansion can be given by:
[tex]\rm \Delta V\;=\;\beta V\Delta T[/tex]
where, [tex]\Delta[/tex]V is the expansion of volume, V is the initial volume, [tex]\beta[/tex] is the coefficient of volume expansion, and [tex]\Delta[/tex]T is the change in temperature.
The change in volume for mercury:
[tex]\Delta[/tex]V = 1.80 [tex]\rm \times\;10^-^4\;K^-^1[/tex] [tex]\times[/tex] 1000 [tex]\rm cm^3[/tex] [tex]\times[/tex] (52.0 [tex]\rm ^\circ C[/tex] - 0.80 [tex]\rm ^\circ C[/tex] )
[tex]\Delta[/tex]V = 9.18 [tex]\rm cm^3[/tex].
Since due to heating, the glass has been expanded, and the volume of mercury overflown has been after the expansion.
Expansion of glass = expansion of mercury - the overflow of mercury
Expansion of glass = 9.18 [tex]\rm cm^3[/tex] - 8.50 [tex]\rm cm^3[/tex]
Expansion of glass = 0.93 [tex]\rm cm^3[/tex]
Since the value of [tex]\Delta[/tex]V = 0.93 [tex]\rm cm^3[/tex], [tex]\Delta[/tex]T = 51.2 [tex]\rm ^\circ C[/tex], and Volume = 1000 [tex]\rm cm^3[/tex] , the coefficient of expansion for glass can be calculated as:
[tex]\beta[/tex] = [tex]\rm \dfrac{0.93}{1000\;\times\;51.2}[/tex] [tex]\rm K^-^1[/tex]
[tex]\beta[/tex] = 1.8 [tex]\rm \times\;10^-^5\;K^-^1[/tex]
The coefficient of expansion for glass has been calculated as 1.8 [tex]\rm \times\;10^-^5\;K^-^1[/tex].
For more information about the coefficient of expansion, refer to the link:
https://brainly.com/question/15796511
