(a) Explanation Express initial partial pressure. P ν 1 = ϕ 1 P g 1 = ϕ 1 P sat@10°C (I) Here, relative humidity at state 1 is ϕ 1 , initial vapor pressure is P g 1 and saturation pressure at temperature of 10°C is P sat@10°C . Express initial partial pressure. P a 1 = P 1 − P ν 1 (II) Here, initial pressure is P 1 . Express initial specific volume. v 1 = R a T 1 P a 1 (III) Here, universal gas constant of air is R a and initial temperature is T 1 . Express initial humidity ratio. ω 1 = ω 2 = 0.622 P ν 1 P 1 − P ν 1 (IV) Here, final humidity ratio is ω 2 . Express initial enthalpy. h 1 = c p T 1 + ω 1 h g 1 (V) Here, initial specific enthalpy at saturated vapor is h g 1 , specific heat at constant pressure of air is c p and temperature at state 1 is T 1 . Express final specific enthalpy. h 2 = c p T 2 + ω 2 h g 2 (VI) Here, final specific enthalpy at saturated vapor is h g 2 and final humidity ratio is ω 2 . Express initial mass flow rate of dry air. m ˙ a 1 = ν ˙ 1 v 1 (VII) Here, initial volume rate is ν ˙ 1 . Express the rate of heat transfer in the heating section. Q ˙ in = m ˙ a 1 ( h 2 − h 1 ) (VIII) Conclusion: Refer Table A-2, “ideal-gas specific heats of various common gases”, and write the gas constant and specific heat at constant pressure of air. R a = 0.287 kPa ⋅ m 3 / kg c p = 1.005 kJ / kg ⋅ °C Refer Table A-4, “saturated water-temperature table”, and write the saturation pressure at temperature of 10°C . P sat@10°C = 1.2281 kPa Substitute 0.30 for ϕ 1 and 1.2281 kPa for P sat@10°C in Equation (I). P ν 1 = ( 0.30 ) ( 1.2281 kPa ) = 0.3684 kPa Substitute 95 kPa for P 1 and 0.3684 kPa for P ν 1 in Equation (II). P a 1 = 95 kPa − 0.3684 kPa = 94.63 kPa Substitute 0.287 kPa ⋅ m 3 / kg for R a , 10°C for T 1 and 94.63 kPa for P a 1 in Equation (III). v 1 = ( 0.287 kPa ⋅ m 3 / kg ) ( 10°C ) 94.63 kPa = ( 0.287 kPa ⋅ m 3 / kg ) [ ( 10 + 273 ) K ] 94.63 kPa = ( 0.287 kPa ⋅ m 3 / kg ) ( 283 K ) 94.63 kPa = 0.8583 m 3 / kg dry air Substitute 95 kPa for P 1 and 0 (b) To determine The relative humidity of the air at the exit.

Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684

9th Edition

ISBN: 9781260048667

Author: Yunus A. Cengel Dr.; Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 14.7, Problem 67P

(a)

To determine

The rate of heat transfer in the heating section.

(b)

To determine

The relative humidity of the air at the exit.

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Chapter 14 Solutions

Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684

Ch. 14.7 - What is the difference between dry air and...Ch. 14.7 - What is vapor pressure?Ch. 14.7 - What is the difference between the specific...Ch. 14.7 - Can the water vapor in air be treated as an ideal...Ch. 14.7 - Explain how vapor pressure of the ambient air is...Ch. 14.7 - Is the relative humidity of saturated air...Ch. 14.7 - Moist air is passed through a cooling section...Ch. 14.7 - How will (a) the specific humidity and (b) the...Ch. 14.7 - Prob. 9P Ch. 14.7 - Consider a tank that contains moist air at 3 atm...

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The rate of heat transfer in the heating section.

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The rate of heat transfer in the heating section.

The relative humidity of the air at the exit.

Chapter 14 Solutions