A physics student is determining the air pressure in Pascals by using a mercury

Question

A physics student is determining the air pressure in Pascals by using a mercury barometer. If the height of the liquid is 741 mm, what is the air pressure in the lab? Assuming that the height of the mercury can be read to the nearest 1.0 mm, and that the density of mercury that was used in the calculation is 13.56 g/cm3, and the value of g was 9.8 m/s2, what is the uncertainty in the value? What is the most precise value that can be obtained from the experiment using more precise values for the constants?

Explanation / Answer

pressure = 741 mm Hg, 1000mm= 1m, 741 mm = 741/1000 =0.741 m, density = 13.56 g/cc, 1000gm= 1 kg and 1m3= 10-6 cc, 13.55 g/cc= 13.56* 10-3/10-6 kg/m3=13560 kg/m3

pressure = density*accleration due to gravity* height in m = 13560* 9.8*0.741 N/m2=98470 N/m2

since height can be read to nearest 1 mm

pressure can be =(741+1)/1000* 13560* 9.8 N/m2 =98894 N/m2 or (741-1)/1000*9.8*13560 N/m2= 98337 N/m2

more precise value can be obtained from considering density = 13600 kg/m3 and g= 9.81 m/sec2

pressure = 0.741*13600*9.81 N/m2=98861 N/m2

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