Question

You wish to observe the progress of your vacuum pump in evacuating a tall bell jar for the purpose of demonstrating that sound waves do not travel in a vacuum. So you place a mercury barometer inside the bell jar and follow the height of the mercury column as the pump chugs away. When you observe a height of 6.27 mm, what fraction of atmospheric pressure, expressed as a percentage, have you achieved in your bell jar? The density of mercury is 1.36 × 104 kg/m3 and standard atmospheric pressure is 1.01 × 105 Pa.

Answer 1

Atmospheric Pressure is given by:

Patm = 1.01*10^5 Pa

Now Pressure achieved in bell jar is given by:

P = rho*g*h

rho = density of mercury = 1.36*10^4 kg/m^3

g = 9.81 m/sec^2

h = height in bell jar = 6.27 mm = 6.27*10^-3 m

Now fraction of pressure in bell jar and atmospheric pressure will be:

N = (1.36*10^4*9.81*6.27*10^-3)/(1.01*10^5)

N = 0.00828

Now in percentage

N = 0.00828*100%

N = 0.828%

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