Question

Normal atmospheric pressure is 1.013 105 Pa. The approach of a storm causes the height of a mercury barometer to drop by 27.1 mm from the normal height. What is the atmospheric pressure? (The density of mercury is 13.59 g/cm3.)

Answer 1

To calculate the atmospheric pressure, we can use the formula: Pressure = Density × Acceleration due to gravity × Height. Given the density of mercury, the height difference, and the acceleration due to gravity, we can calculate the atmospheric pressure.

Step-by-step explanation:

The normal atmospheric pressure is 1.013 × 10^5 Pa. In this case, the height of a mercury barometer drops by 27.1 mm due to the approaching storm. To calculate the atmospheric pressure, we can use the formula:

Pressure = Density × Acceleration due to gravity × Height

Given that the density of mercury is 13.59 g/cm3, the height difference is 27.1 mm, and the acceleration due to gravity is approximately 9.8 m/s2, we can calculate the atmospheric pressure:

Pressure = (13.59 g/cm3)(9.8 m/s2)(27.1 mm)

Answer 2

The atmospheric pressure is
`0.97622*10^(5)\ Pa`.

Step-by-step explanation:

Given that,

Atmospheric pressure
`P_(atm)= 1.013*10^(5)\ Pa`

drop height h'= 27.1 mm

Density of mercury
`\rho= 13.59 g/cm^3`

We need to calculate the height

Using formula of pressure

`p = \rho g h`

Put the value into the formula

`1.013*10^(5)=13.59*10^(3)*9.8* h`

`h =(1.013*10^(5))/(13.59*10^(3)*9.8)`

`h=0.76\ m`

We need to calculate the new height

`h''=h - h'`

`h''=0.76-27.1*10^(-3)`

`h''=0.76-0.027`

`h''=0.733\ m`

We need to calculate the atmospheric pressure

Using formula of atmospheric pressure

`P=\rho g h`

Put the value into the formula

`P= 13.59*10^(3)*9.8*0.733`

`P=0.97622*10^(5)\ Pa`

Hence, The atmospheric pressure is
`0.97622*10^(5)\ Pa`.