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Mechanical Properties Of Fluids

Question
CBSEENPH11019701

What is the relative humidity of air when the room temperature is 16°C and the dew point is 7.4°C? Given that the saturated vapour pressure at 7°C, 8°C and 16°C is 7.5mm, 8mm and 13.5mm respectively of mercury.

Solution

Given,
Room temperature, T = 16°C

Dew point temperature, T0 = 7.4°C

SVP at 7°C = 7.5mm of Hg

SVP at 8°C = 8mm of Hg

SVP at 16°C = 13.5mm of Hg

For a small change in temperature, it can be assumed that saturated vapour pressure changes linearly.
The saturated vapour pressure increases by 0.5 mm for one degree rise in temperature.
Therefore increase in saturated vapour pressure for 0.4°C increase in temperature will be 0.2mm of mercury.
Hence, the saturated vapour pressure at dew point i.e. 7.4°C is 7.7 mm of mercury.
Now the relative humidity is,
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