Question

Use a table for the Vapor Pressure of Water to answer the following. Report temperatures to the nearest 5 ^oC and pressures to the nearest 0.1 torr.
a) What are the pressure of water and the dew point in a system in which the relative humidty is 43.0% at 40 ^oC?

Pressure of water =	torr
Dew Point =	oC

b) The pressure of water vapor in the atmosphere is found to be 17.5 when it is 30 ^oC. What are the dew point and relative humidty?

Dew Point =	oC
Relative Humidity =	%

Answer 1

Relative humidity= 100*(partial pressure of water vapor/vapor pressrue of liquid)

Antoine equation for water is log Psat(mm Hg)= 8.07131-1730.63/(t+233.426), t in deg.c, psat is vapor pressure of water.

at 40 deg.c, log Psat (mm Hg)= 8.07131- 1730.63/(40+233.426), Psat= 55.19 mm Hg=55.19 Torr

partial pressure of water vapor= 0.43* vapor presure of water= 0.43*55.19 mmHg ( torr ) =23.73 mm Hg (torr)

dew point is defined as the pressure at which the partial pressure of water vapor= vapor pressure of liquid at the given temperatrue.

hence vapor pressure = 23.73 mm Hg, substituting this value in Antoine equation gives the dew point.

log (23.73 )= 8.07131-1730.63/(t+233.426), t= 25.03, the dew point.

2. At 30 deg.c, vapor pressure of water can be calculated from log Psat(mm Hg)= 8.07131-1730.63/(30+233.426), psat= 31.7 mm HG

relative humidity = 100* partial pressure of water vapor/vapor pressure of liquid at the given temperature = 100*17.5/31.7 = 55.2%

dew point is the temperature at which the partial pressure = vapor pressure

Hence from Antoine equation, log (17.5)= 8.07131-1730.63/(t+233.426), t=20.02 deg.c