The following table gives the experimentally measured volume per gram of mercury

Question

The following table gives the experimentally measured volume per gram of mercury as a function of temperature. Use the data to estimate the error in the temperature measured by mercury in glass thermometer which has been calibrated only at 0oC and 100oC. Fill the following table to show the difference.

10

I have tried a few different equations and my answers do not make sense. The TA of the Thermodynamics course gave me those several answers above and mine were around 11.1 cm3/g

T(oC) Volume (cm3/g) Estimated Value (cm3/g) Difference (cm3/g) 0 0.0735560 0.0735560 0

10

0.0736893 0.0736902 0.0000009 20 0.0738233 0.0738244 0.0000011 30 0.0739572 0.0739586 0.0000014 40 0.0740910 0.0740928 0.0000018 50 0.0742250 60 0.0743592 70 0.0744936 80 0.0746282 90 0.0747631 100 0.0748981

Explanation / Answer

Variation of Density with Temperature can be approximated well. Given by

Density = 13.596 - 0.00246 Tm g/cm^3

where Tm is Temp. in degree Celsius at which density is to be calculated

at 0 degree, Density = 13.596 - 0.00246 * 0 = 13.596 g/cm^3

Specific volume = 1/13.596 = 0.0735510 cm^3/g

Error = 0.0735560 - 0.0735510 = 0.000005 cm^3/g

Similary for 10 degree Celsius, Density = 13.596 - 0.00246 * 10 = 13.5714 g/cm^3

Specific volume = 1/13.5714 = 0.0736844 cm^3/g

Error = 0.0736893 - 0.0736844 = 0.0000049 cm^3/g

Similary for 20 degree Celsius, Density = 13.5468 g/cm^3

Specific volume = 0.0738182 cm^3/g

Error = 0.0738233 - 0.0738182 = 0.0000051 cm^3/g

Similarly, for all values of temperature, Specific Volume can be calculated.

For T = 100 Degree celsius, Density = 13.596 - 0.00246 * 100 = 13.35 g/cm^3

Specific Volume = 1/13.35 = 0.0749064 cm3^/g

Error = 0.0748981 - 0.0749064 = - 0.0000083 cm^3/g

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