Question

Late on an autumn day, the relative humidity is 45.0% and the temperature is $20.0^\circ\textrm{C}$ . What will the relative humidity be that evening when the temperature has dropped to $10.0^\circ\textrm{C}$, assuming constant water vapor density?

Final Answer

$82.3 \%$

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Video Transcript

This is College Physics Answers with Shaun Dychko.
We know that relative humidity is the vapor density divided by the saturation vapor density. So, we'll figure out what the vapor density is by multiplying both sides by the saturation vapor density and we'll end up with vapor density is the relative humidity of 0.45 which is 45 percent converted into a decimal. And then multiplied by the saturation vapor density at 20 degrees Celsius which is 17.2 grams per cubic meter. And that means the vapor density is 7.74 grams per cubic meter. Now, this vapor density doesn't change with temperature, it's only the saturation or the maximum vapor density that changes with temperature. So this 7.74 grams per cubic meter is still the vapor density at ten degree Celsius. And so then, we'll calculate the relative humidity at ten degrees. And so at 7.74 grams per cubic meter divided by the maximum possible vapor density known as the saturation density of 9.4 grams per cubic meter at ten degrees Celsius. And this gives us relative humidity of 82.3 percent.