Question

The volume of a glass vessel is 1000 cc at \[20^\circ C\]. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are $1.8 \times {10^{ - 4}}{^\circ }{\text{C and }}9 \times {10^{ - 6}}{^\circ }{\text{C}}$ respectively.
Option
A.100 cc
B.10 cc
C.500 cc
D.5 cc

Answer 1

Hint: In chemistry, 1 cc equals 1 cubic centimetre. It is roughly equivalent to 1 ml, and any expression may be used. In the case of syringes, 1cc is the norm. The amount of the material filling the room in the calculation instrument is denoted by cc.

Complete answer:
Thermal expansion, which does not include phase transitions, is the tendency of matter to change its form, area, volume, and density in response to a change in temperature. The total molecular kinetic energy of a material is a monotonic property of temperature. When a fluid is heated, the molecules tend to vibrate and travel more, resulting in a greater distance between them. It's rare to see substances that contract as the temperature rises, and they only happen at a certain temperature level.
Now we assume the volume of mercury added at \[20^\circ C\] be \[{V_m}\]
Hence at\[20^\circ C\], the volume of the space remaining is 1000 - \[{V_m}\] --- (1)
As a result of thermal expansion, the volume now varies as follows:
Glass vessel volume = \[{V_g}^2 = 1000(1 + 9 \times {10^{ - 6}}\theta )\]
Mercury volume = \[{V_m}^2 = {V_m}(1 + 1.8 \times {10^{ - 4}}\theta )\]
where $\theta$ is the change in temperature
Volume of remaining space = \[{V_g}^2 - {V_m}^2 = 1000 - {V_m} + 9 \times {10^{ - 6}}\theta - 1.8{V_m} \times {10^{ - 4}}\theta \;\] --- (2)
Equating 1 and 2
\[{V_m} = \dfrac{{9 \times {{10}^{ - 6}}}}{{1.8 \times {{10}^{ - 4}}}}\]= 500 cc

Note:
The difference in volume per unit volume caused by a change in temperature is known as the Coefficient of Cubical Thermal Expansion.
The term "linear expansion" refers to a difference in one dimension (length) rather than a change in volume (volumetric expansion).
The area thermal expansion coefficient compares a change in temperature to a change in the area dimensions of a material. The fractional difference in area per degree of temperature change is what this term refers to.