(a)
The high relative humidity and the low relative humidity of the places.
(a)
Answer to Problem 52PQ
The high relative humidity of the place is
Explanation of Solution
Given that the high temperature is
Relative humidity is the ratio of the partial pressure of water to the saturated vapor pressure of water. The value of partial pressure of water is not given directly, but the value can be derived using the information given in the question. The dew point of the place is given, which is the temperature at which the partial pressure of water equals to the saturated vapor pressure.
Write the expression to convert temperature from Fahrenheit scale to Celsius scale.
Here,
Refer table 20.5 which gives the saturated vapor pressure values for various temperatures.
From the table look for the values for the high temperature and the low temperature. But the values of vapor pressure for both the temperatures is not available. So use the values for temperatures
Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between
Here,
Now the rate of change of vapor pressure with respect to the change of temperature is found. Now using this value, the vapor pressure of water at
Write the interpolation expression for vapor pressure at the dew point.
Here,
The vapor pressure at the dew point is equal to the vapor pressure of water.
Use expression (V) in (VI) for
Similarly write expression for finding vapor pressure for high temperature using the values of
Here,
Similarly write expression for finding vapor pressure for low temperature using the values of
Here,
Write the expression to find the relative humidity at high temperature.
Here,
Write the expression to find the relative humidity at low temperature.
Here,
Conclusion:
Substitute
Substitute
Substitute
From the table 20.5, vapor pressure at
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the high relative humidity of the place is
(b)
Whether dews form or not in the places.
(b)
Answer to Problem 52PQ
Yes, dews are formed in the atmosphere of the places.
Explanation of Solution
Dews are formed by the condensation of water. Dew point of Minneapolis and Minnesota is
Conclusion:
Therefore, dews can be formed at Minneapolis and Minnesota.
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Chapter 20 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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