# Calculating sensible heat, latent heat, and heat of vaporization of water

A 1000 m3/min air flow at 170 degrees F and containing 60% relative humidity needs to be cooled to 48 degrees F to promote condensation of the water vapor in the air.

How would you calculate the sensible heat, the latent heat, and determine the latent heat of vaporization of the water vapor in this air stream as the air is cooled from 170 F to 48 F??

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Problem:

A 1000 m3/min air stream contains 60% moisture content (humidity) --- the air is at 180 degrees F to start and is to be cooled to 48 degrees F. Assume atmospheric pressure.

How do I calculate the sensible and latent heat to determine the needed cooling.

Also, what would the latent heat of vaporization be for water vapor --- and is determined at 180 degrees or 48 degrees F.

Ultimately I'm trying to determine how much cooling is needed to condense the water vapor and the mass of the water vapor actually condensed?

Solution:

We will work in metrical system of units. Finally, we can convert in British system.

Given:

Volumetric flow rate:

Inlet temperature:

Outlet temperature:

Pressure (constant): p0 = 1.013 bar

Relative humidity: = 60%

Since the air is not saturated in water vapors, the amount of vapors behaves like the superheated steam. The partial pressure of these vapors in the air mixture is:

(1)

where ps1 = saturation pressure corresponding to T1.

From Steam Tables, we find on the saturation line at T1 = 355.4 K:

(2)

where h = specific enthalpy, = density, v = specific volume (v = 1/)

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#### Solution Summary

This solution explains how to calculate sensible heat, latent heat and determine the latent heat.