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Kinetic Theory — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsKinetic Theory4 Marks
Question
On a winter day, the outside temperature is 0°C and relative humidity 40%. The air from outside comes into a room and is heated to 20°C. What is the relative humidity in the room? The saturation vapour pressure at 0°C is 4.6mm of mercury and at 20°C it is 18mm of mercury.
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Answer

Relative humidity = 40% SVP = 4.6mm of Hg$0.4=\frac{\text{VP}}{4.6}\Rightarrow\text{VP}=0.4\times4.6=1.84$
$\frac{\text{P}_1\text{V}}{\text{T}_1}=\frac{\text{P}_2\text{V}}{\text{T}_2}\Rightarrow\frac{1.84}{273}=\frac{\text{P}_2}{293}$
$\Rightarrow\text{P}_2=\frac{1.84}{273}\times293$
Relative humidity at 20°C$=\frac{\text{VP}}{\text{SVP}}=\frac{1.84\times293}{273\times10}=0.109=10.9\%$

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