Question 13 of 36intermediate🔧 ApplyNumerical3 marks

Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below: 1 Pa = 1 N m⁻² If mass of air at sea level is 1034 g cm⁻², calculate the pressure in pascal.

Correct Answer

The pressure at sea level is 1.01332×1051.01332 \times 10^5 Pa.

Exercise: EXERCISES | Q: 1.13 | (Page 26)
For More Understanding

Explanation

To find the pressure in pascal, the given mass of air per unit area must be converted into SI base units of kg m⁻². Then, using the relation that pressure is force per unit area (where force is mass multiplied by acceleration due to gravity, g=9.8 m s−2g = 9.8 \text{ m s}^{-2}), the pressure can be calculated in N m⁻², which is equivalent to pascal.

Solution Steps

  1. Step 1: Convert the given mass of air into SI units (kg m⁻²). Given mass = 1034 g cm−21034 \text{ g cm}^{-2} Using the relations 1 kg=1000 g1 \text{ kg} = 1000 \text{ g} (so 1 g=10−3 kg1 \text{ g} = 10^{-3} \text{ kg}) and 1 cm=10−2 m1 \text{ cm} = 10^{-2} \text{ m} (so 1 cm−2=104 m−21 \text{ cm}^{-2} = 10^{4} \text{ m}^{-2}):

    1034 g cm−2=1034×(10−3 kg)×(104 m−2)=10340 kg m−21034 \text{ g cm}^{-2} = 1034 \times (10^{-3} \text{ kg}) \times (10^{4} \text{ m}^{-2}) = 10340 \text{ kg m}^{-2}

  2. Step 2: Calculate the force per unit area (pressure). Pressure is determined as force per unit area of the surface. Force (FF) = mass ×\times acceleration due to gravity (g=9.8 m s−2g = 9.8 \text{ m s}^{-2}).

    P=FA=m×gA=(10340 kg m−2)×(9.8 m s−2)=101332 N m−2P = \frac{F}{A} = \frac{m \times g}{A} = (10340 \text{ kg m}^{-2}) \times (9.8 \text{ m s}^{-2}) = 101332 \text{ N m}^{-2}

  3. Step 3: Express the final pressure in pascal. Given that 1 Pa=1 N m−21 \text{ Pa} = 1 \text{ N m}^{-2}, the pressure is 101332 Pa101332 \text{ Pa}, which can also be written as 1.01332×105 Pa1.01332 \times 10^5 \text{ Pa}.

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