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Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).
Correct answer is '0.85 to 0.88'. Can you explain this answer?
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Assuming ISA standard sea level conditions (288.16 K, density of 1.225...
Calculating the Density of Air at Leh
To calculate the density of air at an altitude of 3500 m above mean sea level in Leh, we can use the ideal gas law along with the information provided in the question.
Ideal Gas Law
The ideal gas law is given by the equation:
\[PV = nRT\]
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the universal gas constant
- T is the temperature of the gas
Calculations
Given that the temperature at sea level (288.16 K) and the altitude (3500 m), we can calculate the temperature at Leh using the standard lapse rate of 6.5°C per 1000 m altitude increase.
\[T_{Leh} = 288.16 - (6.5 \times 3.5) = 265.41 K\]
Next, we can calculate the pressure at Leh using the hydrostatic equation:
\[P_{Leh} = P_{sea} \times e^{\left(\frac{-M \times g \times h}{R \times T_{sea}}\right)}\]
Where:
- M is the molar mass of air
- g is the acceleration due to gravity
- h is the altitude difference
- T_{sea} is the temperature at sea level
Finally, we can calculate the density of air at Leh using the ideal gas law:
\[density_{Leh} = \frac{P_{Leh}}{R \times T_{Leh}}\]
Result
After performing the calculations, the density of air at Leh is approximately 0.85 to 0.88 kg/m3, which is lower than the density at sea level due to the decrease in pressure and temperature at higher altitudes.
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Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer?
Question Description
Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer?.
Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).Correct answer is '0.85 to 0.88'. Can you explain this answer?.
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