The high relative humidity and the low relative humidity of the places.

Question

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Answer 1

Question

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

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Answer 2

Question

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

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Answer 3

Question

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

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Answer 4

Question

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

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Answer 5

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

Answer 6

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

Answer 7

Chapter 20, Problem 52PQ

(a)

To determine

The high relative humidity and the low relative humidity of the places.

Answer 8

(a)

Expert Solution

Answer to Problem 52PQ

The high relative humidity of the place is 108%_, and the low relative humidity is 60%_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given that the high temperature is 21°F, low temperature is 3°F, and the dew point is 5°F.

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.

T(°C)=59(T(°F)−32) (I)

Here, T(°C) is the temperature in Celsius scale, and T(°F) is the temperature in Fahrenheit scale.

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 −25°C and 0°C, interpolate between these points to get the corresponding value for the given high temperature and low temperature of the place.

Write the expression for the rate of change of saturated vapor pressure with respect to the change in temperature between 0°C and −25°C.

ΔPsvpΔT=Psvp0−Psvp25T0−T25 (IV)

Here, ΔPsvpΔT is the rate of change of saturated vapor pressure with respect to temperature, Psvp0 is the saturated vapor pressure at temperature T0, Psvp25 is the saturated vapor pressure at temperature T25, T0 and T25 are the upper and lower limits of temperatures considered for interpolation.

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 5°F can be found using interpolation formula.

Write the interpolation expression for vapor pressure at the dew point.

PD=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (V)

Here, PD is the vapor pressure in Celsius scale at the dew point, and TD is the dew temperature.

The vapor pressure at the dew point is equal to the vapor pressure of water.

Pwater=PD (VI)

Use expression (V) in (VI) for Pwater.

Pwater=Pspv0+(TD−T0)(Pspv25−Pspv0T25−T0) (VII)

Similarly write expression for finding vapor pressure for high temperature using the values of 0°C and 25°C.

PH=Pspv0+(TH−T0)(Pspv25−Pspv0T25−T0) (VIII)

Here, PH is the vapor pressure corresponding to the high temperature, and TH is the high temperature in Celsius scale.

Similarly write expression for finding vapor pressure for low temperature using the values of 0°C and 25°C.

PL=Pspv0+(TL−T0)(Pspv25−Pspv0T25−T0) (IX)

Here, PL is the vapor pressure for low temperature, and TL is the low temperature in Celsius scale.

Write the expression to find the relative humidity at high temperature.

RHH=PwaterPH×100% (X)

Here, RHH is the relative humidity at high temperature.

Write the expression to find the relative humidity at low temperature.

RHL=PwaterPL×100% (XI)

Here, RHL is the relative humidity at low temperature.

Conclusion:

Substitute 21°F for T(°F) in equation (I) to find T(°C) corresponding to the high temperature.

TH(°C)=59(21−32)=−6°C

Substitute 3°F for T(°F) in equation (I) to find T(°C) corresponding to the low temperature.

TL(°C)=59(3−32)=−16°C

Substitute 5°F for T(°F) in equation (I) to find T(°C) corresponding to the dew point.

TD(°C)=59(5−32)=−15°C

From the table 20.5, vapor pressure at 0°C is 610.3 Pa, and at −25°C is 70.11 Pa.

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, and −25°C for T25 in equation (IV) to find ΔPsvpΔT.

ΔPsvpΔT=(610.3 Pa−70.11 Pa)0°C−(−25°C)=21.6 Pa/°C

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −15°C for TD in equation (VII) to find Pwater.

Pwater=610.3 Pa+(−15°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=286.3 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −6°C for TH in equation (VIII) to find PH.

PH=610.3 Pa+(−6°C−0°C)(70.11 Pa−610.3 Pa−25°C−−0°C)=480.7 Pa

Substitute 610.3 Pa for Pspv0, 70.11 Pa for Pspv25, 0°C for T0, −16°C for TL in equation (IX) to find PL.

PL=610.3 Pa+(−16°C−0°C)(70.11 Pa−610.3 Pa−25°C−(−0°C))=264.7 Pa

Substitute 286.3 Pa for Pwater, and 480.7 Pa for PH in equation (X) to find RHH.

RHH=286.3 Pa480.7 Pa×100%=60%

Substitute 286.3 Pa for Pwater, and 264.7 Pa for PL in equation (XI) to find RHL.

RHL=286.3 Pa264.7 Pa×100%=108%

Therefore, the high relative humidity of the place is 108%_, and the low relative humidity of the place is 60%_.

Answer 13

(b)

To determine

Whether dews form or not in the places.

(b)

Expert Solution

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 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.

Answer 14

(b)

To determine

Whether dews form or not in the places.

Answer 15

(b)

Expert Solution

Answer to Problem 52PQ

Yes, dews are formed in the atmosphere of the places.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Dews are formed by the condensation of water. Dew point of Minneapolis and Minnesota is 5°F which is equal to −15°C. Dews are formed at a temperature of −16°C. This is below the dew point of these places. The relativity humidity at this temperature is more than hundred percentage. This indicates that the amount of water vapor in the air is very high and they can be condensed to form dews at this place.

Conclusion:

Therefore, dews can be formed at Minneapolis and Minnesota.