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If the relative humidity is 90.0% on a muggy summer morning when the temperature is 20.0ºC , what will it be later in the day when the temperature is 30.0ºC , assuming the water vapor density remains constant?

50.9$\%$

Physics 101 Mechanics

Chapter 13

Temperature, Kinetic Theory, and the Gas Laws

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Lectures

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so we know that the percent relative humidity would be equaling the vapor density divided by the saturation vapor density. And so we can then say that this would be over other times 100. And so we can then say that we're going to consider the relative humidity a 20 degrees Celsius and that of 30 degrees Celsius, and so the ratio of the relative humidity. We can say the percent relative humidity for 30 degrees Celsius, divided by the percent relative humidity for 20 degrees Celsius. This would be equal. We could say the vapor density at 30 degree Celsius, divided by the ah vapor debts. The saturation vapor density at 30 degree Celsius multiplied by 100. This would be divided by the vapor density at 20 degrees Celsius, divided by the saturation vapor density at 20 degrees Celsius multiplied by again 100. And so we can then say that this is gonna be equal the percent relative humidity, 30 degrees Celsius, divided by again. The percent relative humidity at 20 degrees Celsius is gonna be equal to the saturation vapor density at 20 degree Celsius, divided by the saturation vapor density at 30 degrees Celsius. and this is gonna be equaling. Two point died multiplied by we can say 17.2 grams per cubic meter, divided by 30.4 grams per cubic meter. And so this is equaling 50 0.9 percent because we know that essentially, rather were it would more. Don't make it more clear this would be equal to this. But then we would have to find the percent relative humidity at 30 degrees Celsius. This would be equal to the percent relative humidity at 20 degrees Celsius, which we know is 90% so 900.90 and then multiplied by 17.2, divided by 30.4 grams per cubic meter. And so we find that the percent relative humidity at 30 degrees Celsius is equaling 50.9%. And so this would be our final answer. That is the end of the solution. Thank you for

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