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Chapter 7: Problem 1061

When the room temperature becomes equal to the dew point the relative humidity of the room is (A) \(100 \%\) (B) \(0 \%\) (C) \(70 \%\) (D) \(85 \%\)

Short Answer

Expert verified
When the room temperature becomes equal to the dew point, it means the air is saturated and cannot hold any more moisture. In this situation, the relative humidity is \(100\%\), as the partial pressure of water vapor is equal to the saturation vapor pressure. So, the correct answer is (A) \(100\%\).

Step by step solution

01

Understand Relative Humidity

Relative humidity (RH) is a measure of how full of water vapor the air is relative to the maximum amount of water vapor the air can hold at a given temperature. It is expressed as a percentage and calculated using the formula: \(Relative\ Humidity = \frac{Partial\ Pressure\ of\ Water\ Vapor}{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature} \times 100\%\)
02

Understand Dew Point

The dew point is the temperature at which the air is saturated, meaning it has reached its maximum capacity to hold moisture. If the air temperature cools further, the excess moisture will condense out as precipitation or dew.
03

Calculate Relative Humidity at Dew Point

When the room temperature becomes equal to the dew point, it means the air is saturated, and the partial pressure of water vapor is equal to the saturation vapor pressure. Putting this information into the relative humidity formula: \(Relative\ Humidity = \frac{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature}{Saturation\ Vapor\ Pressure\ at\ the\ same\ temperature} \times 100\% = 100\%\)
04

Finding the Answer

Since the relative humidity when the room temperature becomes equal to the dew point is 100%, the correct answer is: (A) \(100\%\)

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