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

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

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

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

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

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.

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

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

For 0.01701 bar water vapor pressure, dew point temperature is 15°C.

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

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 m_{3} / 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

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

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 / m^{3} of dry air

b) 0.01216 g / m^{3} of dry air

c) 0.01216 m^{3} / m^{3} of dry air

d) 0.01216 kg / kg of dry air

View Answer

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 / m

^{3}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

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

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

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}.

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

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}.

15. If the relative humidity is zero, then the humidity ratio is infinity.

a) False

b) True

View Answer

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.

**Sanfoundry Global Education & Learning Series – Refrigeration & Air Conditioning.**

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