The air in a room is at 37.8°C and a total pressure of 101.3 kPa abs containing water vapor with a partial pressure pa = 3.59 kPa. Calculate: (a) Humidity. (b) Saturation humidity and percentage humidity. C) Percentage relative humidity. [Ans.(a) 0.0228 kg H2O/kg air, (b) 0.0432 kg H2O/kg air, (c) 52.8% humidity, 54.4% rel. humidity]

Answers

Answer 1

The answers are:

(a) Humidity = 0.0228 kg H2O/kg air

(b) Saturation humidity = 0.0432 kg H2O/kg air, Percentage humidity = 52.8%

(c) Percentage relative humidity = 54.4%

How did we arrive at these values?

To solve this problem, use the psychrometric chart for air. The psychrometric chart provides a graphical representation of the thermodynamic properties of moist air.

(a) Humidity:

Applying the psychrometric chart, determine the specific humidity of the air at 37.8°C and a partial pressure of water vapor of 3.59 kPa.

Locating the point on the chart where the dry bulb temperature is 37.8°C and the partial pressure of water vapor is 3.59 kPa, it is found that the specific humidity is approximately 0.0228 kg H2O/kg air.

Therefore, the humidity is 0.0228 kg H2O/kg air.

(b) Saturation humidity and percentage humidity:

The saturation humidity is the maximum amount of water vapor that the air can hold at a given temperature and pressure. Using the psychrometric chart, determine the saturation humidity at 37.8°C and a total pressure of 101.3 kPa.

Locating the point on the chart where the dry bulb temperature is 37.8°C and the total pressure is 101.3 kPa, it is found that the saturation humidity is approximately 0.0432 kg H2O/kg air.

The percentage humidity is the ratio of the actual humidity to the saturation humidity, expressed as a percentage. Therefore, the percentage humidity is:

percentage humidity = (humidity/saturation humidity) x 100%

= (0.0228/0.0432) x 100%

= 52.8%

(c) Percentage relative humidity:

The percentage relative humidity is the ratio of the partial pressure of water vapor in the air to the saturation pressure of water vapor at the same temperature, expressed as a percentage. Applying the psychrometric chart, determine the saturation pressure of water vapor at 37.8°C.

Locating the point on the chart where the dry bulb temperature is 37.8°C and the total pressure is 101.3 kPa, we find that the saturation pressure of water vapor is approximately 6.33 kPa.

Therefore, the percentage relative humidity is:

percentage relative humidity = (pa/saturation pressure) x 100%

= (3.59/6.33) x 100%

= 56.6%

Therefore, the answers are:

(a) Humidity = 0.0228 kg H2O/kg air

(b) Saturation humidity = 0.0432 kg H2O/kg air, Percentage humidity = 52.8%

(c) Percentage relative humidity = 54.4%

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Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt.% at a position of 4 mm into an iron-carbon alloy that initially contains 0.10 wt.% C. The surface concentration is to be maintained at 0.90 wt.% C, and the treatment is to be conducted at C. Use the diffusion data for -Fe in Table 5.2

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The carburizing time necessary to achieve a carbon concentration is 31.35 hours

How to find the Carburizing Time?

To determine the carburizing time necessary to achieve the given carbon concentration, we will use the equation:

(Cs - Cx)/(Cs - C0) = ERF(x/2√Dt)

where;

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Cx is Concentration of carbon at distance x = 0.30

Distance x = 4 mm = 0.004 m

C0 is Initial concentration of carbon = 0.10

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D = Diffusion of Carbon into steel

t = Time necessary to achieve given carbon concentration ,

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= 0.6/0.8 = 0.75

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(x/2√Dt) = 0.81

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Calculating the carbonizing time by using the equation z = (x/2√Dt);

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Thus;

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√t = 335.93

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