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If the atmospheric pressure at sea level is 7.5 N/cm2, determine the pressure at a height of 3000m assuming the pressure variation follows isothermal law. The density of air is given as 1.2 km/m3.
- a)4.68 N/cm2
- b)9.37 N/cm2
- c)2.34 N/cm2
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the atmospheric pressure at sea level is 7.5 N/cm2, determine the p...
Explanation: pressure at any height Z = p*e-gZ/RT
=75000*e -9.81*3000*1.2/75000
= 4.68 N/cm2.
=75000*e -9.81*3000*1.2/75000
= 4.68 N/cm2.
Most Upvoted Answer
If the atmospheric pressure at sea level is 7.5 N/cm2, determine the p...
Given data:
Atmospheric pressure at sea level, P1 = 7.5 N/cm²
Height, h = 3000 m
Density of air, ρ = 1.2 kg/m³
Assumption: Pressure variation follows isothermal law, which states that the pressure decreases at a constant rate with an increase in altitude.
Formula: P2 = P1 × e^(-mg/ρRT)
where,
P2 = pressure at height h
m = mass of air per unit area
g = acceleration due to gravity
R = gas constant
T = temperature
Calculation:
The mass of air per unit area can be calculated as:
m = ρ × h
The temperature of air can be assumed as constant at 15°C = 288 K.
The gas constant for air is R = 287 J/kg.K.
Substituting the given values in the formula, we get:
P2 = 7.5 × e^(-9.81 × 3000/(1.2 × 287 × 288))
P2 = 4.68 N/cm²
Therefore, the pressure at a height of 3000 m is 4.68 N/cm².
Hence, option (a) is correct.
Atmospheric pressure at sea level, P1 = 7.5 N/cm²
Height, h = 3000 m
Density of air, ρ = 1.2 kg/m³
Assumption: Pressure variation follows isothermal law, which states that the pressure decreases at a constant rate with an increase in altitude.
Formula: P2 = P1 × e^(-mg/ρRT)
where,
P2 = pressure at height h
m = mass of air per unit area
g = acceleration due to gravity
R = gas constant
T = temperature
Calculation:
The mass of air per unit area can be calculated as:
m = ρ × h
The temperature of air can be assumed as constant at 15°C = 288 K.
The gas constant for air is R = 287 J/kg.K.
Substituting the given values in the formula, we get:
P2 = 7.5 × e^(-9.81 × 3000/(1.2 × 287 × 288))
P2 = 4.68 N/cm²
Therefore, the pressure at a height of 3000 m is 4.68 N/cm².
Hence, option (a) is correct.
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If the atmospheric pressure at sea level is 7.5 N/cm2, determine the pressure at a height of 3000m assuming the pressure variation follows isothermal law. The density of air is given as 1.2 km/m3.a)4.68 N/cm2b)9.37 N/cm2c)2.34 N/cm2d)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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