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Question

The atmospheric pressure at zero elevation is given as 1.01325×105 N/m2. What is the pressure at an elevation of 3 km? Given, molecular weight of air =28 g/mol and temperature of air is constant at 300 K. Also, acceleration due to gravity, g=10 m/s2.

A
0.64×105 N/m2
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B
105 N/m2
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C
0.7235×105 N/m2
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D
2×105 N/m2
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Solution

The correct option is C 0.7235×105 N/m2
Pressure variation of a gas at higher elevation is given by
P=P0emghRT .....(1)
Given,
Pressure at zero elevation (P0)=1.01325×105 N/m2
Molecular weight of gas (m)=28×103 kg/mol
Temperature of gas (T)=300 K
Height at which pressure is to be determined (h)=3000 m
So, by substituting the given data in (1),
P=1.01325×105×e28×103×10×30008.315×300
=0.7235×105 N/m2
Thus, option (c) is the correct answer.

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