Question

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

Answer 1

Answer : The correct option is, (A)
`0.002010812m^3`

Solution : Given,

Volume of mercury at
`20^oC` is
`0.002m^3`

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

Formula used for the volume expansion of liquid,

`V_(T)=v_(1)[1+\gamma (T_(2)-T_(1))]`

or,

`V_(2)=V_(1)[1+\gamma (T_(2)-T_(1))]`

where,

`V_(T)` = volume of liquid at temperature
`T^oC`

`V_(1)` = volume of liquid at temperature
`20^oC`

`V_(2)` = volume of liquid at temperature
`50^oC`

`\gamma` = volume expansion coefficient of mercury at
`20^oC` is 0.00018 per centigrade

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

`V_(2)=0.002[1+0.00018(50-20)]=0.0020108m^3`

Therefore, the volume of mercury at
`50^oC` is,
`0.0020108m^3`

Answer 2

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