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At a temperature of 10oC the percent relative humidity is R10 , and at 40oC it is R40. At each of these temperatures the partial pressure of water vapor in the air is the same. Using the vapor pressure curve for water that accompanies this problem, determine the ratio R10 / R40 of the two humidity values. (Cutnell 357)

User Irio
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2 Answers

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Final answer:

The percent relative humidity at 10°C would be 100%, as this is the dew point temperature. The relative humidity at 40°C would be lower due to higher saturation vapor pressure at that temperature. However, the exact ratio of R10 to R40 cannot be provided without the saturation vapor density at 40°C.

Step-by-step explanation:

The question involves understanding percent relative humidity and how it varies with temperature in the context of physics. Relative humidity is the amount of water vapor present in the air expressed as a percentage of the amount needed for saturation at the same temperature. Since the partial pressure of water vapor is the same at both temperatures (10°C and 40°C), but the saturation vapor pressure is higher at 40°C, the relative humidity will be lower at 40°C compared to 10°C. Therefore, the ratio R10 / R40 represents the ratio of the percent relative humidity at both temperatures.

Given the vapor density is 9.40 g/m³ at both temperatures and using Table 13.5, the saturation vapor density at 10.0°C is also 9.40 g/m³, indicating that the relative humidity, R10, is 100%. However, at 40°C the saturation vapor density is higher. The ratio R10 / R40 can be calculated using the saturation vapor density values at both temperatures. Without the actual vapor density values at 40°C, the exact ratio cannot be given, but the concept and method to determine it is clear.

User Iker Solozabal
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Answer:


(R_(10) )/(R_(40) ) = 5

Step-by-step explanation:

Using the Vapor pressure of water versus temperature curve:

At Relative humidity,
R_(10), with equivalent temperature of 10⁰C, the partial vapor pressure,
p_(vs) = 1300 Pa

At Relative humidity,
R_(40) with equivalent temperature of 40⁰C, the partial vapor pressure,
p_(vs) = 6500 Pa


(R_(10) )/(R_(40) ) = (p_(vs) at 10^(0) C)/(p_(vs) at 40^(0) C) \\(R_(10) )/(R_(40) ) = 6500/1300\\(R_(10) )/(R_(40) ) = 5

User EngineerSpock
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