Question

In one observation, the column in a mercury barometer (as is shown in Figure) has a measured heighth of $\mathbf{740}\mathbf{.}\mathbf{35}\mathbf{}\mathit{m}\mathit{m}$. The temperature is$\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{°}C$, at which temperature the density of mercury role="math" localid="1657193277146" $\mathit{\rho }$is $\mathbf{1}\mathbf{.}\mathbf{3608}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{}\mathit{k}\mathit{g}\mathbf{/}{\mathit{m}}^{\mathbf{3}}$. The free-fall acceleration g at the site of the barometer is $\mathbf{9}\mathbf{.}\mathbf{7835}\mathbf{}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$. What is the atmospheric pressure at that site in Pascal and in torr (which is the common unit for barometer readings)?

Short answer

1. Atmospheric pressure at that site in Pascal is$98565.66\mathrm{Pa}$
2. Atmospheric pressure at that site in torr is$739.26\mathrm{torr}$

Step-by-step solution

The given data

Measured height$h=740.35\mathrm{mm}$

Density of mercury,$\mathrm{\rho }=1.3608\times {10}^4\mathrm{kg}/{\mathrm{m}}^3$

Free fall acceleration at site of barometer, $g=9.7835\mathrm{m}/{\mathrm{s}}^2$

Understanding the concept of pressure 

To find pressure, we can use the formula in terms of density, acceleration, and height. We can convert the pressure from Pascal to torr using the conversion factor.

Formula:

Pressure applied on a body, (i)

$1\mathrm{torr}=133.33\mathrm{Pa}$

 Calculation of pressure in Pascal

Atmospheric pressure in Pascal using equation (i) is given as:

$$\begin{gathered} p=1.3608\times {10}^4\mathrm{kg}/{\mathrm{m}}^3\times 9.7835\mathrm{m}/{\mathrm{s}}^{2}x0.74035\mathrm{m} \\ =98565.66\mathrm{Pa}.....................................\left(\mathrm{a}\right) \end{gathered}$$

Hence, the value of pressure in Pascal is$98565.66Pa$

b) Calculation of pressure in torr

From equation (a), we get the pressure, hence

$$\begin{gathered} p=98565.66\mathrm{Pa}\times \frac{1\mathrm{torr}}{133.33\mathrm{Pa}}(\because 1\mathrm{torr}=133.33\mathrm{Pa}) \\ =739.26\mathrm{torr} \end{gathered}$$

Hence, the value of pressure in torr is role="math" localid="1657194537605" $739.26\mathrm{torr}$.