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In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value?
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In an isothermal atmosphere, the pressure A) is constant with elevatio...
Explanation:
An isothermal atmosphere is a hypothetical atmosphere in which the temperature remains constant with altitude. In such an atmosphere, the pressure decreases with altitude, but the rate of decrease is not constant. The pressure decrease is related to the density decrease with altitude.
The Pressure-Altitude Relationship:
The relationship between pressure and altitude in an isothermal atmosphere is given by the barometric formula, which states that the pressure at any altitude is given by:
P = P0 * e-(gM/RT)h
Where P is the pressure at the altitude h, P0 is the pressure at sea level, g is the acceleration due to gravity, M is the molar mass of the air, R is the universal gas constant, and T is the temperature of the atmosphere.
The Pressure Gradient:
The pressure gradient is the rate of change of pressure with altitude. In an isothermal atmosphere, the pressure gradient is given by:
dp/dh = - (gM/RT) * P
Where dp/dh is the pressure gradient, g is the acceleration due to gravity, M is the molar mass of the air, R is the universal gas constant, T is the temperature of the atmosphere, and P is the pressure at the altitude h.
The Variation of Pressure with Altitude:
The pressure decreases with altitude in an isothermal atmosphere, but the rate of decrease is not constant. At low altitudes, the pressure decreases rapidly with altitude, but as the altitude increases, the rate of decrease of pressure decreases. Near the surface, the pressure decreases rapidly because the density of the air is high and the weight of the air above compresses the air below. As the altitude increases, the density of the air decreases, and the weight of the air above also decreases, resulting in a decrease in the rate of decrease of pressure with altitude. At very high altitudes, the pressure approaches a constant value, which is the pressure of the vacuum.
Conclusion:
In an isothermal atmosphere, the pressure decreases with altitude, but the rate of decrease is not constant. Near the surface, the pressure decreases rapidly, but as the altitude increases, the rate of decrease of pressure decreases. At very high altitudes, the pressure approaches a constant value, which is the pressure of the vacuum.
An isothermal atmosphere is a hypothetical atmosphere in which the temperature remains constant with altitude. In such an atmosphere, the pressure decreases with altitude, but the rate of decrease is not constant. The pressure decrease is related to the density decrease with altitude.
The Pressure-Altitude Relationship:
The relationship between pressure and altitude in an isothermal atmosphere is given by the barometric formula, which states that the pressure at any altitude is given by:
P = P0 * e-(gM/RT)h
Where P is the pressure at the altitude h, P0 is the pressure at sea level, g is the acceleration due to gravity, M is the molar mass of the air, R is the universal gas constant, and T is the temperature of the atmosphere.
The Pressure Gradient:
The pressure gradient is the rate of change of pressure with altitude. In an isothermal atmosphere, the pressure gradient is given by:
dp/dh = - (gM/RT) * P
Where dp/dh is the pressure gradient, g is the acceleration due to gravity, M is the molar mass of the air, R is the universal gas constant, T is the temperature of the atmosphere, and P is the pressure at the altitude h.
The Variation of Pressure with Altitude:
The pressure decreases with altitude in an isothermal atmosphere, but the rate of decrease is not constant. At low altitudes, the pressure decreases rapidly with altitude, but as the altitude increases, the rate of decrease of pressure decreases. Near the surface, the pressure decreases rapidly because the density of the air is high and the weight of the air above compresses the air below. As the altitude increases, the density of the air decreases, and the weight of the air above also decreases, resulting in a decrease in the rate of decrease of pressure with altitude. At very high altitudes, the pressure approaches a constant value, which is the pressure of the vacuum.
Conclusion:
In an isothermal atmosphere, the pressure decreases with altitude, but the rate of decrease is not constant. Near the surface, the pressure decreases rapidly, but as the altitude increases, the rate of decrease of pressure decreases. At very high altitudes, the pressure approaches a constant value, which is the pressure of the vacuum.
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In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value?.
In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an isothermal atmosphere, the pressure A) is constant with elevation B) decreases linearly with elevation C) cannot be related to elevation D) decreases near the surface but approaches a constant value?.
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