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Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube manometer connected to the vessel shows a reading of 70 cm of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325 bar, acceleration due to gravity is 9.81 m/s2 and density of mercury is 13600 kg/m3. The mass of nitrogen (in kg) in the vessel is _______.
(Important - Enter only the numerical value in the answer)
Correct answer is '4.55'. Can you explain this answer?
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Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube ...
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To find the mass of nitrogen in the vessel, we need to consider the pressure and temperature conditions inside the vessel.
First, let's calculate the pressure exerted by the nitrogen gas inside the vessel. The pressure can be determined using the manometer reading and the density of mercury.
Given:
Height of mercury column in the U-tube manometer = 70 cm = 0.7 m
Density of mercury = 13600 kg/m^3
Acceleration due to gravity = 9.81 m/s^2
The pressure exerted by the nitrogen gas can be calculated using the formula:
Pressure = Atmospheric pressure + (Density of mercury * g * Height difference)
Using the given values:
Pressure = 1.01325 bar + (13600 kg/m^3 * 9.81 m/s^2 * 0.7 m)
Converting the pressure to pascals:
1 bar = 100,000 pascals
Pressure = (1.01325 * 100,000) + (13600 * 9.81 * 0.7) pascals
Next, we can use the ideal gas law to find the number of moles of nitrogen gas present in the vessel. The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant
T = Temperature
Rearranging the equation to solve for n:
n = PV / RT
Using the given values:
Pressure = calculated pressure from above
Volume = 2 m^3
Universal gas constant = 8314 J/kmol-K
Temperature = 288 K
Substituting the values into the equation:
n = (Pressure * Volume) / (Universal gas constant * Temperature)
Finally, to find the mass of nitrogen in the vessel, we need to multiply the number of moles by the molar mass of nitrogen. The molar mass of nitrogen is approximately 28 g/mol.
Mass of nitrogen = Number of moles * Molar mass of nitrogen
Substituting the values into the equation:
Mass of nitrogen = n * 28 g/mol
Converting grams to kilograms, we get the final answer:
Mass of nitrogen in the vessel = (n * 28) / 1000 kg
Calculating these values will give us the answer of 4.55 kg.
First, let's calculate the pressure exerted by the nitrogen gas inside the vessel. The pressure can be determined using the manometer reading and the density of mercury.
Given:
Height of mercury column in the U-tube manometer = 70 cm = 0.7 m
Density of mercury = 13600 kg/m^3
Acceleration due to gravity = 9.81 m/s^2
The pressure exerted by the nitrogen gas can be calculated using the formula:
Pressure = Atmospheric pressure + (Density of mercury * g * Height difference)
Using the given values:
Pressure = 1.01325 bar + (13600 kg/m^3 * 9.81 m/s^2 * 0.7 m)
Converting the pressure to pascals:
1 bar = 100,000 pascals
Pressure = (1.01325 * 100,000) + (13600 * 9.81 * 0.7) pascals
Next, we can use the ideal gas law to find the number of moles of nitrogen gas present in the vessel. The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant
T = Temperature
Rearranging the equation to solve for n:
n = PV / RT
Using the given values:
Pressure = calculated pressure from above
Volume = 2 m^3
Universal gas constant = 8314 J/kmol-K
Temperature = 288 K
Substituting the values into the equation:
n = (Pressure * Volume) / (Universal gas constant * Temperature)
Finally, to find the mass of nitrogen in the vessel, we need to multiply the number of moles by the molar mass of nitrogen. The molar mass of nitrogen is approximately 28 g/mol.
Mass of nitrogen = Number of moles * Molar mass of nitrogen
Substituting the values into the equation:
Mass of nitrogen = n * 28 g/mol
Converting grams to kilograms, we get the final answer:
Mass of nitrogen in the vessel = (n * 28) / 1000 kg
Calculating these values will give us the answer of 4.55 kg.
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Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube manometer connectedto the vessel shows a reading of 70 cm of mercury (level higher in the end open toatmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325bar, acceleration due to gravity is 9.81 m/s2 and density of mercury is 13600 kg/m3. The massof nitrogen (in kg) in the vessel is _______.(Important - Enter only the numerical value in the answer)Correct answer is '4.55'. Can you explain this answer?
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Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube manometer connectedto the vessel shows a reading of 70 cm of mercury (level higher in the end open toatmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325bar, acceleration due to gravity is 9.81 m/s2 and density of mercury is 13600 kg/m3. The massof nitrogen (in kg) in the vessel is _______.(Important - Enter only the numerical value in the answer)Correct answer is '4.55'. 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 Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube manometer connectedto the vessel shows a reading of 70 cm of mercury (level higher in the end open toatmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325bar, acceleration due to gravity is 9.81 m/s2 and density of mercury is 13600 kg/m3. The massof nitrogen (in kg) in the vessel is _______.(Important - Enter only the numerical value in the answer)Correct answer is '4.55'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Temperature of nitrogen in a vessel of volume 2 m3 is 288 K. A U-tube manometer connectedto the vessel shows a reading of 70 cm of mercury (level higher in the end open toatmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325bar, acceleration due to gravity is 9.81 m/s2 and density of mercury is 13600 kg/m3. The massof nitrogen (in kg) in the vessel is _______.(Important - Enter only the numerical value in the answer)Correct answer is '4.55'. Can you explain this answer?.
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