Psychrometry Questions and Answers

Answer: B

On heating at constant pressure, relative humidity decreases, but specific humidity remains unchanged.

Specific humidity is the mass of water vapour per unit mass of dry air. Heating a fixed mass of mixture adds no water and removes none, so it stays the same, and at constant total pressure the vapour partial pressure stays the same too.

Relative humidity is the vapour partial pressure divided by the saturation pressure at the mixture's temperature. The saturation pressure rises steeply with temperature, so the relative humidity falls. That is why heated air feels drier. Any option in which specific humidity changes is wrong, since no moisture is added or condensed.

Answer: D

The relative humidity is about 81.80%.

Saturation pressure at 30°C, then the actual vapour pressure from the humidity, using 18/29 = 0.6207:

\[ \begin{aligned} \ln p_{w}^{0} &= 18.6556 - \frac{5217.635}{303} = 1.4357 \\ p_{w}^{0} &= 4.203\ \text{kPa} \\ p_{w} &= \frac{0.0218(101.325)}{0.6207 + 0.0218} = 3.438\ \text{kPa} \\ RH &= \frac{3.438}{4.203} = 81.8\% \end{aligned} \]

The other options do not follow from the given humidity and vapour pressure equation.

Answer: A

The enthalpy of the moist air is about 85.93 kJ/kg of dry air.

Taking 0°C liquid water as the reference, the enthalpy is the sensible heat of the dry air plus that of the vapour, including its latent heat:

\[ \begin{aligned} h &= c_{a}T + H(\lambda_{0} + c_{v}T) \\ &= 1.005(30) + 0.0218(2502.3 + 1.884 \times 30) \\ &= 30.15 + 55.78 = 85.93\ \text{kJ/kg} \end{aligned} \]

Most of it is the latent heat carried by the water vapour. 31.38 kJ/kg is roughly the dry air term with the vapour's sensible heat only, which forgets the latent heat. The other values do not follow from the data.

Answer: D

The relative humidity is about 71 %.

The specific humidity is the mass of vapour per unit mass of dry air:

\[ \begin{aligned} \omega &= \frac{0.5}{35} = 0.01429 \\ &= \frac{0.622\,p_{v}}{p-p_{v}} \end{aligned} \]

Solving for the vapour pressure with p = 100 kPa:

\[ \begin{aligned} p_{v} &= \frac{\omega p}{0.622+\omega} = \frac{1.429}{0.6363} \\ &= 2.245\ \text{kPa} \\ \phi &= \frac{2.245}{3.17} = 0.708 \approx 71\ \% \end{aligned} \]

The relative humidity compares the actual vapour pressure with the saturation pressure at the same temperature, so the 3.17 kPa enters only in the last step. 67 %, 55 % and 83 % do not follow from the specific humidity of 0.0143.

Answer: B

The perpendicular axis represents specific humidity.

A psychrometric chart plots dry-bulb temperature on the horizontal axis and specific humidity (humidity ratio, kg of vapour per kg of dry air) on the vertical axis.

Wet-bulb temperature, relative humidity and enthalpy are shown as families of lines or curves drawn across the chart, not as the axis perpendicular to dry-bulb temperature.

Answer: B

The ratio is \(\frac{3}{7}\).

For an insulated steady mixing chamber with constant \(c_{p}\), the enthalpy given up by the warm stream equals that gained by the cold stream:

\[ \begin{aligned} \dot{m}_{c}c_{p}(24 - 10) &= \dot{m}_{a}c_{p}(30 - 24) \\ \frac{\dot{m}_{c}}{\dot{m}_{a}} &= \frac{6}{14} = \frac{3}{7} \end{aligned} \]

\(7/3\) is the inverse ratio, \(\dot{m}_{a}/\dot{m}_{c}\). \(2/7\) and \(4/7\) do not satisfy the energy balance. The values of \(c_{p}\) and \(\gamma\) cancel and are not needed.

Answer: B

Conventionally, the moisture content is taken as the ordinate and the temperature as the abscissa.

On the standard psychrometric chart (the paper spells it 'psychometric'), dry-bulb temperature is plotted along the horizontal axis and humidity ratio (moisture content, kg of water per kg of dry air) along the vertical axis, usually on the right-hand side. Lines of relative humidity, wet-bulb temperature, enthalpy and specific volume are drawn across this grid.

Option A reverses the axes. Wind speed and time do not appear on a psychrometric chart at all.

Answer: A

The chart is used to represent the state of moist air.

A psychrometric chart shows the thermodynamic properties of air-water vapour mixtures at a given total pressure. Any two known properties, such as dry-bulb and wet-bulb temperature, fix a point on the chart, from which the others (humidity ratio, relative humidity, dew point, enthalpy, specific volume) can be read. It is used to design and analyse drying, cooling and air conditioning.

It does not show air speed, and atmospheric pressure is held constant for a given chart, not represented on it. 'Potential energy in the air' is not one of its properties.