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Coefficient of volume expansion of mercury is \[0.18 \times {10^ {- 3}} {/^0} C\]. If the density of mercury at ${0^0} C $ is $13.6gc{c^ {- 1}} $ then its density at ${200^0} C $ is:
A) $13.11gc{c^{ - 1}}$
B) $52.11gc{c^{ - 1}}$
C) $16.11gc{c^{ - 1}}$
D) $26.11gc{c^{ - 1}}$

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Last updated date: 13th Jun 2024
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Answer
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Hint: A body when exposed to a temperature change it changes its dimensions. If the change in temperature is positive i.e. there is an increase of temperature then the body undergoes expansion or in other words the dimensions of the body increase. This expansion is called thermal expansion and is directly proportional to the change in temperature.

Complete step by step solution:
Thermal expansion continues to adjust the volume in response to a temperature change. For example, atoms and molecules oscillate continuously about their balancing point. (The buckling of the railway track as seen in). Thermal motion is known as this type of arousal. The component particles tend to move further as the material is heated, retaining an average separation from neighbouring particles. The degree of expansion divided by the temperature fluctuations is called the thermal expansion coefficient of the material which varies with the temperature in general.

The expansion of alcohol in a thermometer is one of many frequently found examples of thermal expansion, the change in size or volume of a given mass with temperature. Hot air rises when its volume increases, which allows the hot air’s mass to be less than the density of surrounding air, creating a buoyant (upward) effect on the hot air. The same goes for all liquids and gases which transfers natural warmth in homes, oceans and weather systems upwards. Thermal expansion also affects solids. For one, tracks and bridges have expansion joints, such that temperature changes can be readily extended and contracted.

Coefficient of volume expansion is \[0.18 \times {10^{ - 3}}{/^0}C\] and Density of Mercury at ${0^0}C$ is $13.6gc{c^{ - 1}}$.
Now, formula for density is,
$\rho = \dfrac{{{\rho _0}}} {{1 + {r_0} t}} $
Where,
$\rho $ is Density at any temperature other than${0^0} C$
${\rho _0} $ is Density at ${0^0} C$
${r_0} $ is a coefficient of volume expansion.
$t$ is the temperature at which density is to be calculated.
 Hence,
\[\rho = \dfrac{{13.6}}{{1 + 0.18 \times 200}}\]
$\rho = 13.11gc{c^ {- 1}} $

Note: Objects can usually grow as temperatures rise. A variety of heating materials however contract within such temperature ranges; this is generally called negative thermal expansion, instead of thermal contracture. Water is the major exception to the rule of law. Owing to the peculiar existence of the hydrogen bond in water, the water has this special attribute.