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If a certain mass of mercury has a volume of 0.002 m3 at a temperature of 20°C, what will be the volume at 50°C?

A. 0.002010812m3

B. 0.004021624m3

C. 0.002021624m3

D. 0.000010812m3

Respuesta :

metchelle
By using the combined gas law which says that P1V1/T1 = P2V2/T2, assuming constant pressure, the volume at the required temperature can be obtained.((0.002 m3)(50+273.15))/(20+273.15) = volume 2 at 50 degrees C.
This gives the answer 0.0022048 m3

Answer : The correct option is, (A) [tex]0.002010812m^3[/tex]

Solution : Given,

Volume of mercury at [tex]20^oC[/tex] is [tex]0.002m^3[/tex]

As mercury is a liquid. So, we have to apply the volume of expansion of liquid.

Formula used for the volume expansion of liquid,

[tex]V_{T}=v_{1}[1+\gamma (T_{2}-T_{1})][/tex]

or,

[tex]V_{2}=V_{1}[1+\gamma (T_{2}-T_{1})][/tex]

where,

[tex]V_{T}[/tex] = volume of liquid at temperature [tex]T^oC[/tex]

[tex]V_{1}[/tex] = volume of liquid at temperature [tex]20^oC[/tex]

[tex]V_{2}[/tex] = volume of liquid at temperature [tex]50^oC[/tex]

[tex]\gamma[/tex] = volume expansion coefficient of mercury at [tex]20^oC[/tex] is 0.00018 per centigrade

Now put all the given values in the above formula, we get

[tex]V_{2}=0.002[1+0.00018(50-20)]=0.0020108m^3[/tex]

Therefore, the volume of mercury at [tex]50^oC[/tex] is, [tex]0.0020108m^3[/tex]

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