Relative humidity is one of the very important parameter which expresses the condition of air. Relative humidity is expresses as a percentage value. If relative humidity of is too high, it means there are high water content in air and that is uncomfortable for human body. In this tutorial, we will discuss what is relative humidity and solve example problems with detailed answers.
Content
Humidity is expressed in two ways, relative humidity and absolute humidity. Relative humidity is expressed as a percentage and absolute humidity is expressed as moisture content per unit volume.
In this tutorial, we first look definitions and equations of relative humidity and then discuss the problems.
When air is saturated, air cannot hold more water vapor and start to condense as liquid water.
With time, water amount in the tank increases. After sometime, increment of water amount in the tank stops and comes to a constant value. We call that saturated state is gained by the system. Now, air holds the maximum amount of water vapor.
Until saturated state is gained, water vapor pressure increases and comes to constant pressure value if temperature is not changed.
the amount of water vapor present in air expressed as a percentage of the amount needed for saturation at the same temperature.
Relative humidity does not have units and it depends on temperature. Relative humidity is expressed as a percentage.
Relative humidity equation is expressed in two ways, from amount (mass) and vapor pressure.
Saturated vapor pressure increases with increase of temperature.
When temperature increases, saturated water vapor pressure increases. Then look the equation of relative humidity which was expressed in pressure terms. In that equation, saturated vapor pressure term is below the division. So, when that number decreases ( with temperature decrement), related humidity value increases until air gets saturated.
But remember that, absolute humidity remains constant while relative humidity decreases.
Problem 1
A closed space contains 47.7 g of water vapor. If additional 12.5 of water vapor is provided to the closed space, system become saturated.
Answer
Problem 2
A room contains 72 g of water vapor. Volume of room is 9 m^{3} and temperature is 25^{0}C. Calculate the relative humidity of room. Room is sealed and no mass transfer is allowed.
Data: Saturated water vapor pressure at 25^{0}C = 3.17 kPa
Answer
We know the saturated water vapor pressure at 25^{0}C. Only thing we need to know is actual water vapor pressure of the room.
We can calculate actual water vapor pressure of the room by using PV = nRT equation,
Amount of water can be found by following equation.
Substitute those values in PV = nRT equation assuming that water vapor behave as an ideal gas.
Now, we know the actual water vapor pressure.
Problem 3
A tank has 1m^{3} volume and contains air inside it. At the beginning, tank is at 50^{0}C temperature and it is started to cool upto to 20^{0}C. Initial relative humidity (RH) is 80% and at 20^{0}C, air is saturated due to cooling process. Calculate followings.
You are provided following data.
Answer
When air is cooled, relative humidity increases because water vapor amount needed for saturation is also decreased. At one point, air is saturated from water vapor. Then, with furthermore cooling, water vapor starts to condense to liquid water. With that, mass of water vapor in the air decreases.
First, mass of water vapor (m_{1}) in the initial air should be calculated. Then final mass of water vapor (m_{2}) is calculated. Difference between m_{1} and m_{2} is the answer. ( m_{1} > m_{2} )
Condensed Water Vapor Mass = m_{1} - m_{2}
Relative humidity (RH) = Water Vapor Pressure (P) / Saturated Water Vapor Pressure (P^{0})
RH = P/P0
State 1
State 2
Apply PV = mRT for water vapor
P_{1} = 9.737 kPa
Apply PV = mRT for water vapor
P_{2} = 2.737 kPa
Condensed water vapor mass = m_{1} - m_{2}
Condensed water vapor mass = 48 g
We have solved above problem from equations. Also we can use psychrometric chart to solve this problem very easily. If you did not learn psychrometric chart, learn how to read psychrometric chart and its axes.
Questions
Air conditioner does the job of removing water vapor when water vapor content is higher than expected level to keep comfortable environment.
If you want to raise relative humidity (RH) at same temperature, you have increase the water vapor pressure by adding some water to the space. You can calculate the required amount of water to raise RH from following steps.
If you know the relative humidity and temperature of the air, you can calculate the water vapor mass in several steps of calculations.
When you know the relative humidity, you can calculate actual water vapor pressure.
See the above defined equation of relative humidity.
Actual water vapor pressure = (related humidity * water vapor pressure of saturated air)/100
Then apply the gas law to find out more he water vapor mass in considering volume.
Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system.
Relation of relative humidity formula with vapor pressure
relative humidity = (actual vapor pressure / vapor pressure)*100
Relative humidity is expressed as a percentage.
Saturated air cannot hold more water vapor. If temperature increased, air can take more water vapor. Also if temperature is incresed and there is no more water to evaporate, humidity decreases.
Humidity is defined as the the concentration of water vapour present in the air. Water vapur is formed due to evaporation of liquid water. Humidity can be changed time to time or place to place.
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