Psychrometric Relations Questions and Answers

This set of Air-Conditioning Multiple Choice Questions & Answers (MCQs) focuses on “Psychrometric Relations”.

1. What is the value of humidity ratio if p_v = 0.387 bar and p_a = 0.997 bar?
a) 0.482
b) 0.241
c) 0.122
d) 0.622
View Answer

Answer: b
Explanation: Humidity ratio is the mass of water vapor present in 1 kg of dry air and has a unit g / kg of dry air.
W = 0.622 p_v / p_a
= 0.622 x 0.387 / 0.997
= 0.241 kg / kg of dry air.

2. What is the value of humidity ratio if m_v = 1.423 and m_a = 3.589?
a) 0.1
b) 0.2
c) 0.4
d) 0.5
View Answer

Answer: c
Explanation: Humidity ratio is the mass of water vapor present in 1 kg of dry air and has a unit g / kg of dry air. It is also defined as the ratio of the mass of water vapor to the mass of dry air in a given volume of the air-vapor mixture. Hence, it is given as m_v/ m_a.
W = 1.423 / 3.589 = 0.396 ≅ 0.4.

3. What is the value of relative humidity if m_v = 2.901 and m_s = 9.056?
a) 0.300
b) 0.330
c) 0.310
d) 0.320
View Answer

Answer: d
Explanation: Relative humidity is the ratio of actual mass of water vapor in a given volume of moist air to the mass of water vapor in the same volume of saturated air. It can be represented as,
∅ = m_v / m_s = p_v / p_s = 2.901 / 9.056 = 0.320.

4. What is the value of relative humidity if p_v = 0.468 bar and p_s = 0.893 bar?
a) 52 %
b) 54 %
c) 56 %
d) 190 %
View Answer

Answer: a
Explanation: Relative humidity is the ratio of actual mass of water vapor in a given volume of moist air to the mass of water vapor in the same volume of saturated air. It can be represented as,
∅ = m_v / m_s = p_v / p_s = 0.468 / 0.893 = 0.524 = 52.4 %.

5. What is the value of p_b if p_a = 1.48 bar and p_v = 1.52 bar, according to Dalton’s law of partial pressures?
a) 1 bar
b) 2 bar
c) 3 bar
d) 4 bar
View Answer

Answer: c
Explanation: The Dalton’s law states that the total pressure exerted by the mixture of air and water vapor is equal to the sum of the pressures, which each constituent would exert if it occupied the same space by itself. Mathematically, it can be represented as, p_b = p_a + p_v = 1.48 + 1.52 = 3 bar.

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6. If DBT = 30°C, WBT = 20°C and Barometer reading is 740 mm of Hg. Find out DPT using steam tables.
a) 5°C
b) 35°C
c) 15°C
d) 25°C
View Answer

7. If DBT = 30°C, WBT = 20°C and Barometer reading is 740 mm of Hg. Find out relative humidity using steam tables.
a) 40 %
b) 50 %
c) 30 %
d) 20 %
View Answer

Answer: a
Explanation: For given conditions, pressure corresponding to WBT from steam table is p_w = 0.02337 bar
p_b = 740 mm of Hg = 740 x 133.3 / 100000 = 0.98642 bar
Pressure of water vapor = p_v = p_w – [(p_b – p_w) (t_d – t_w) / 1544 – 1.44 t_w]
= 0.02337 – [(0.98642 – 0.02337) (30 – 20) / 1544 – 1.44 x 20]
= 0.01701 bar
Saturation pressure for given DBT is p_s = 0.04242 bar
Relative humidity = p_v / p_s = 0.01701 / 0.04242 = 0.40 = 40 %.

8. If DBT = 30°C, WBT = 20°C and Barometer reading is 740 mm of Hg. Find out specific humidity using steam tables.
a) 10.914 m₃ / kg of dry air
b) 10.914
c) 10.914 kg / kg of dry air
d) 10.914 g / kg of dry air
View Answer

Answer: d
Explanation: For given conditions, pressure corresponding to WBT from steam table is p_w = 0.02337 bar
p_b = 740 mm of Hg = 740 x 133.3 / 100000 = 0.98642 bar
Pressure of water vapor = p_v = p_w – [(p_b – p_w) (t_d – t_w) / 1544 – 1.44 t_w]
= 0.02337 – [(0.98642 – 0.02337) (30 – 20) / 1544 – 1.44 x 20]
= 0.01701 bar
Specific humidity = W = 0.622 p_v / p_b – p_v = 0.622 x 0.01701 / 0.98642 – 0.01701 = 10.914 g / kg of dry air.

9. If DBT = 30°C, WBT = 20°C and Barometer reading is 740 mm of Hg. Find out degree of saturation using steam tables.
a) 40 %
b) 39 %
c) 38 %
d) 35 %
View Answer

Answer: b
Explanation: For given conditions, pressure corresponding to WBT from steam table is p_w = 0.02337 bar
p_b = 740 mm of Hg = 740 x 133.3 / 100000 = 0.98642 bar
Pressure of water vapor = p_v = p_w – [(p_b – p_w) (t_d – t_w) / 1544 – 1.44 t_w]
= 0.02337 – [(0.98642 – 0.02337) (30 – 20) / 1544 – 1.44 x 20]
= 0.01701 bar
Specific humidity = W = 0.622 p_v / p_b – p_v = 0.622 x 0.01701 / 0.98642 – 0.01701 = 10.914 g / kg of dry air
Saturation pressure for given DBT is p_s = 0.04242 bar
W_s = 0.622 p_s / p_b – p_s = 0.622 x 0.004242 / 0.98642 – 0.04242 = 27.945 g / kg of dry air
Degree of saturation, μ = W / W_s = 10.914 / 27.945 = 0.39 = 39 %.

10. If DBT = 30°C, WBT = 20°C and Barometer reading is 740 mm of Hg. Find out vapor density using steam tables.
a) 0.01216 kg / m³ of dry air
b) 0.01216 g / m³ of dry air
c) 0.01216 m³ / m³ of dry air
d) 0.01216 kg / kg of dry air
View Answer

Answer: a
Explanation: For given conditions, pressure corresponding to WBT from steam table is p_w = 0.02337 bar
p_b = 740 mm of Hg = 740 x 133.3 / 100000 = 0.98642 bar
Pressure of water vapor = p_v = p_w – [(p_b – p_w) (t_d – t_w) / 1544 – 1.44 t_w]
= 0.02337 – [(0.98642 – 0.02337) (30 – 20) / 1544 – 1.44 x 20]
= 0.01701 bar
Specific humidity = W = 0.622 p_v / p_b – p_v = 0.622 x 0.01701 / 0.98642 – 0.01701 = 10.914 g / kg of dry air
ρ_v = W (p_b – p_v) / R_a T_d = 0.010914 (0.98642 – 0.01701) 105 / 287 (273 + 30)
= 0.01216 kg / m³ of dry air.

11. What is the humidity ratio in terms of mass?
a) m_v / m_a
b) m_a / m_v
c) p_v / p_a
d) p_a / p_v
View Answer

Answer: a
Explanation: Humidity ratio is the mass of water vapor present in 1 kg of dry air and has a unit g / kg of dry air. It is also defined as the ratio of the mass of water vapor to the mass of dry air in a given volume of the air-vapor mixture. Hence, it is given as m_v / m_a.

12. What is the humidity ratio in terms of pressure?
a) 0.622 p_v / p_b
b) 0.622 p_v / p_a
c) 0.622 m_v / m_b
d) 0.622 m_v / m_a
View Answer

Answer: b
Explanation: Humidity ratio is the mass of water vapor present in 1 kg of dry air and has a unit g / kg of dry air. It is also defined as the ratio of the mass of water vapor to the mass of dry air in a given volume of the air-vapor mixture. Hence, it is given as m_v / m_a = R_a p_v / R_v p_a using ideal gas equation.
R_a = 0.287 and R_v = 0.461 kJ/kg K, putting these values in above equation we get,
W = 0.287 / 0.461 (p_v / p_a)
W = 0.622 p_v / p_a.

13. Relative humidity is represented as __________
a) m_v / m_a
b) m_a / m_v
c) p_s / p_v
d) m_v / m_s
View Answer

14. Which of the following is true, according to Dalton’s law of partial pressures?
a) p_b = p_a x p_v
b) p_b = p_a – p_v
c) p_b = p_a + p_v
d) p_a = p_b + p_v
View Answer

15. If the relative humidity is zero, then the humidity ratio is infinity.
a) False
b) True
View Answer

Answer: a
Explanation: Relative humidity is the ratio of actual mass of water vapor in a given volume of moist air to the mass of water vapor in the same volume of saturated air. It can be represented as,
If, ∅ = m_v / m_s = p_v / p_s = 0,
Then W = 0. So, the humidity ratio is zero if the relative is zero.

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