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c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
CBSE | Class 11 | Mechanical Properties of Fluids | NCERT Exemplar | Physics
c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

Answer:

(c) We know that –

$ p={{p}_{0}}{{e}^{\left( -\frac{{{\rho }_{0}}gh}{{{p}_{0}}} \right)}} $

By substituting the known values, we can determine that

h = 18.43 km

(d) For $ \rho \alpha p $ to work, the temperature in the air must be uniform, which is known as an isothermal environment, which is only attainable near the earth’s surface and not at higher altitudes.

 

 

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