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A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature of air in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at 25°C is 3.17 kPa, the relative humidity of the air in the room is
  • a)
    67%
  • b)
    55%
  • c)
    83%
  • d)
    71%
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A room contains 35 kg of dry air and 0.5 kg of water vapor. The total ...
°C, respectively. Determine the partial pressure of water vapor in the room.

We can use the ideal gas law to solve for the partial pressure of water vapor:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

First, we need to find the number of moles of dry air and water vapor in the room. We can use the molecular weight of each component to convert the masses to moles:

n_dry air = 35 kg / (28.97 g/mol) = 1208.5 mol
n_water vapor = 0.5 kg / (18.02 g/mol) = 27.8 mol

Next, we can find the total volume of the air in the room. We assume that the air behaves as an ideal gas, so we can use the ideal gas law to solve for the volume:

V = nRT/P = (1208.5 + 27.8)(8.314 J/mol-K)(298 K) / (100 kPa * 1000 Pa/kPa) = 342.5 m^3

Now we can find the partial pressure of water vapor using the mole fraction of water vapor:

X_water vapor = n_water vapor / (n_dry air + n_water vapor) = 27.8 / (1208.5 + 27.8) = 0.0226

The partial pressure of water vapor is then:

P_water vapor = X_water vapor * P = 0.0226 * 100 kPa = 2.26 kPa

Therefore, the partial pressure of water vapor in the room is 2.26 kPa.
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A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature ofair in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at25°C is 3.17 kPa, the relative humidity of the air in the room isa)67%b)55%c)83%d)71%Correct answer is option 'D'. Can you explain this answer?
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A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature ofair in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at25°C is 3.17 kPa, the relative humidity of the air in the room isa)67%b)55%c)83%d)71%Correct answer is option 'D'. 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 A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature ofair in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at25°C is 3.17 kPa, the relative humidity of the air in the room isa)67%b)55%c)83%d)71%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature ofair in the room are 100 kPa and 25°C respectively. Given that the saturation pressure for water at25°C is 3.17 kPa, the relative humidity of the air in the room isa)67%b)55%c)83%d)71%Correct answer is option 'D'. Can you explain this answer?.
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