Question Number 210679 by peter frank last updated on 16/Aug/24
Answered by mr W last updated on 16/Aug/24
$${RH}_{\mathrm{16}°{C}} =\frac{\mathrm{273}.\mathrm{15}+\mathrm{16}}{\mathrm{273}.\mathrm{15}+\mathrm{20}}×\frac{\mathrm{17}.\mathrm{5}}{\mathrm{13}.\mathrm{6}}×\mathrm{36\%}\approx\mathrm{46\%} \\ $$
Commented by peter frank last updated on 18/Aug/24
$$\mathrm{thank}\:\mathrm{you} \\ $$
Commented by mr W last updated on 18/Aug/24
$${is}\:{this}\:{correct}? \\ $$
Commented by peter frank last updated on 18/Aug/24
$$\mathrm{thanks}\:\mathrm{mr}\:\mathrm{W} \\ $$
Commented by peter frank last updated on 18/Aug/24
$$\mathrm{its}\:\mathrm{correct} \\ $$
Answered by Spillover last updated on 18/Aug/24
$${Initial}\:{temp}\:\left({T}_{\mathrm{1}} \right)=\mathrm{20}^{°} {C} \\ $$$${Final}\:{temp}\:\left({T}_{\mathrm{2}} \right)=\mathrm{16}^{°} \:{C} \\ $$$${Initia}\:{Relative}\:{humidity}\:{RH}_{\mathrm{1}} =\mathrm{36\%} \\ $$$${Saturation}\:{vapour}\:{pressure}\:\:{at}\:\mathrm{20}°{C}\:{P}_{{sat}\:\mathrm{1}} =\mathrm{17}.\mathrm{5}{mmHg} \\ $$$${Saturation}\:{vapour}\:{pressure}\:{at}\:\mathrm{16}°{C}\:{P}_{{sat}\:\mathrm{2}\:} =\mathrm{13}.\mathrm{6}{mmHg} \\ $$$${Actual}\:{vapour}\:{pressure}\:{at}\:\mathrm{20}°{C} \\ $$$${P}_{{actual}} ={RH}_{\mathrm{1}} ×{P}_{{sat}\mathrm{1}} \\ $$$${P}_{{actual}} =\mathrm{36\%}×\mathrm{17}.\mathrm{5}{mmHg}=\mathrm{6}.\mathrm{3}{mmHg} \\ $$$${Relative}\:{humidity}\:{at}\:\mathrm{16}°{C} \\ $$$${RH}_{\mathrm{2}} =\frac{{P}_{{actual}} }{{P}_{{sat}\:\mathrm{2}} }×\mathrm{100} \\ $$$${RH}_{\mathrm{2}} =\frac{\mathrm{6}.\mathrm{3}}{\mathrm{13}.\mathrm{6}}×\mathrm{100}=\mathrm{46}.\mathrm{3\%} \\ $$$${RH}_{\mathrm{2}} \left({Relative}\:{humidity}\:{at}\:\mathrm{16}°{C}\right)=\mathrm{46}.\mathrm{3\%} \\ $$$$ \\ $$
Commented by mr W last updated on 18/Aug/24
$${why}\:{is}\:{the}\:{P}_{{actual}} \:{the}\:{same}\:{at}\:\mathrm{20}°{C}\: \\ $$$${and}\:{at}\:\mathrm{16}°{C}? \\ $$
Commented by Spillover last updated on 18/Aug/24
$${The}\:{actual}\:{vapour}\:{pressure}\:{remain}\:{the}\:{same} \\ $$$${when}\:{the}\:{temp}\:{changes} \\ $$$$\left({assuming}\:{no}\:{additional}\:{water}\:{vapor}\:{is}\:{added}\right. \\ $$$$\left.{or}\:{removed}\right)\:{becouse}\:{amount}\:{of}\:{water}\:{vapor}\:{in}\: \\ $$$${the}\:{air}\:{does}\:{not}\:{change}\:{when}\:{temp}\:{changes} \\ $$
Commented by Spillover last updated on 18/Aug/24
$$ \\ $$The actual vapor pressure is a measure of the amount of water vapor present in the air. This value is independent of temperature and is determined by how much water vapor is in the air at any given moment.
Commented by peter frank last updated on 18/Aug/24
$$\mathrm{thanks}\:\mathrm{spillover} \\ $$