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?

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