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Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below:
\(1 \mathrm{~Pa}=1 \mathrm{~N} \mathrm{~m}-2\)
If mass of air at sea level is \(1034 \mathrm{~g} \mathrm{~cm}^{-2}\), calculate the pressure in pascal.
\(1 \mathrm{~Pa}=1 \mathrm{~N} \mathrm{~m}-2\)
If mass of air at sea level is \(1034 \mathrm{~g} \mathrm{~cm}^{-2}\), calculate the pressure in pascal.
Solution:
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Verified Answer
Pressure is the force (i.e., weight) acting per unit area
But weight \(=\mathrm{mg}\)
Pressure \(=\) Weight per unit area
\(=1034 \mathrm{~g} \times 9.8 \mathrm{~ms}^{-2} / \mathrm{cm}^2\)
\(=\frac{1034 \mathrm{~g} \times 9.8 \mathrm{~ms}^{-2}}{\mathrm{~cm}^2} \times \frac{1 \mathrm{~kg} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm}}{1000 \mathrm{~g}}\)
\(\times \frac{1 \mathrm{~N}}{1 \mathrm{~m} \times 1 \mathrm{~m}} \times \frac{1 \mathrm{~Pa}}{\mathrm{~kg} \mathrm{~ms}^{-2}}=1.01332 \times 10^5 \mathrm{Nm}^{-2}\)
\(=1.01332 \times 10^5 \mathrm{~Pa}\)
But weight \(=\mathrm{mg}\)
Pressure \(=\) Weight per unit area
\(=1034 \mathrm{~g} \times 9.8 \mathrm{~ms}^{-2} / \mathrm{cm}^2\)
\(=\frac{1034 \mathrm{~g} \times 9.8 \mathrm{~ms}^{-2}}{\mathrm{~cm}^2} \times \frac{1 \mathrm{~kg} \times 100 \mathrm{~cm} \times 100 \mathrm{~cm}}{1000 \mathrm{~g}}\)
\(\times \frac{1 \mathrm{~N}}{1 \mathrm{~m} \times 1 \mathrm{~m}} \times \frac{1 \mathrm{~Pa}}{\mathrm{~kg} \mathrm{~ms}^{-2}}=1.01332 \times 10^5 \mathrm{Nm}^{-2}\)
\(=1.01332 \times 10^5 \mathrm{~Pa}\)
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