Question

How many kilograms of water can be evaporated from a 1 m^2 surface in a lake on a hot summer day, if it is assumed that the limiting factor is solar insolation (1000 W/m^22). Assume that the length of the day is 8 hours and that the air and water temp are at 40 degrees Celsius. B. What volume of air is needed to hold this much water vapor at 40 oC. C. When the sun sets, the air temperature drops to 20 oC. Assuming that the excess water vapor is precipitated as rain, calculate the weight of the rain and the amount of heat released when the water condenses.

A. kilograms of water evaporated were 12.72kg.

B. Molar volume of the water vapor at saturation vapor pressure is ?
and volume of air needed to hold the water is?

C. Weight of the rain at 20 degrees C = _____________________________. Heat released = _____________________________.

show work and assume part A is correct.

Answer 1

A). How many kilograms of water can be evaporated from a 1-m² surface of water in a lake on a hot clear summer day, if it is assumed that the limiting factor of the Sun’s heat of 4 j min^-1 cm^-1 for an 8-hour day? Assume that the air and water temperature remains constant at 40ºC.

answer = 7.99x10^-2 kg/m²

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What volume of air is needed to hold this much water vapor at 40ºC?

Dew point is the temperature at which the water vapor content of the air exceeds saturation and the excess water is squeezed out, forming dew or condensation. The dew point varies with the amount of water vapor in the air. At 40°C, the air can hold no more than 50.7 g/m³ of water vapor.

So, 0.0507 m³ of water vapor can be held by 1 m³ of air.

Therefore, 0.0799 m³ of water vapor is held by 0.0799/ 0.0507 = 1.5759 m³ of air.

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C). When the Sun sets, the air temperature drops to 20ºC. Assuming that the excess water vapor is precipitated as rain, calculate the weight of the rain and the amount of heat released when the water condenses. When it starts raining, do you expect the temperature of the air to rise or fall?

At 20 degree C, the air can hold no more than 17.3 g/m³ of water vapor.

When the temperature drops from 40 degree C to 20 degree C, drop in water vapor content of air = 50.7 – 17.3 = 33.4 g/m³.

This is the mass of rain falling per cubic meter of air.

Latent Heat of condensation of water vapor = 600 cal/gram

Therefore, amount of heat released = 600 cal/g * 33.4 g/m³ = 20040 cal/m³.

When it starts raining, the temperature of the air will fall, because the latent heat is lost in condensing water molecules from vapor state to liquid state.

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