# Calculate Relative Humidity in Air - Definition, Problems and Answers

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

• How to express humidity
• What is saturated air?
• Relative humidity definition - RH
• Relative humidity equations
• Variation of saturated vapor pressure against temperature
• Understand why relative humidity increases when temperature is decreased
• Relative humidity Problems - Questions and Answers

## How to express humidity?

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.

### What is saturated air?

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.

## Relative humidity definition - RH

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 equations

Relative humidity equation is expressed in two ways, from amount (mass) and vapor pressure.

#### Relative humidity equation in water vapor amount (mass) #### Relative humidity equation in water vapor pressure ### Variation of saturated vapor pressure against temperature

Saturated vapor pressure increases with increase of temperature. ### Understand why relative humidity increases when temperature is decreased

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.

## Relative humidity Problems - Questions and Answers

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.

1. What is the requirement of water vapor mass to saturate the closed space?
2. What is the current relative humidity of the space?

• water vapor mass when system is saturated = current water vapor mass + provided water vapor mass
• water vapor mass when system is saturated = 47.7 g + 12.5 g
• water vapor mass when system is saturated = 60.2 g

• relative humidity = water vapor mass in air / water vapor mass for saturation
• water vapor mass when system is saturated = (47.7 g / 60.2 g)*100
• water vapor mass when system is saturated = 79.24 %

A room contains 72 g of water vapor. Volume of room is 9 m3 and temperature is 250C. Calculate the relative humidity of room. Room is sealed and no mass transfer is allowed.

Data: Saturated water vapor pressure at 250C = 3.17 kPa

We know the saturated water vapor pressure at 250C. 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,

• P = actual water vapor pressure, Pa (going to find)
• V = Volume of the room (m3)
• n = amount of water vapor in mol
• R = 8.314 J mol-1 K-1 = gas constant
• T = temperature in Kelvin

Amount of water can be found by following equation.

• Amount (mol) = mass / molar mass
• Amount of water vapor = 72 g / 18 g mol-1
• Amount of water vapor = 4 mol

Substitute those values in PV = nRT equation assuming that water vapor behave as an ideal gas.

• P * 10 m3 = 4 mol * 8.314 J mol-1 K-1 * 298 K
• P = 991.03 Pa
• P = 0.99103 kPa

Now, we know the actual water vapor pressure.

• relative humidity = (actual water vapor pressure / Saturated water vapor pressure) * 100
• relative humidity = (0.99103 / 3.17 ) * 100
• relative humidity = 31.26 %

A tank has 1m3 volume and contains air inside it. At the beginning, tank is at 500C temperature and it is started to cool upto to 200C. Initial relative humidity (RH) is 80% and at 200C, air is saturated due to cooling process. Calculate followings.

1. Total amount of water vapor in the tank in kg at 500C?
2. After saturating, the total condensed mass of water inside the tank?

You are provided following data.

• Water vapor constant (R) = 461.5 J/kg K
• Vapor pressure of water at
• 500C , P10 = 12.171 kPa
• 200C , P20 = 2.302 kPa ### Assumptions you have to make in this question

• Water vapor acts as ideal gas.
• No volume change.

#### Relative humidity increases when temperature decreases.

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 (m1) in the initial air should be calculated. Then final mass of water vapor (m2) is calculated. Difference between m1 and m2 is the answer. ( m1 > m2 )

Condensed Water Vapor Mass = m1 - m2

## Equations of Relative Humidity

Relative humidity (RH) = Water Vapor Pressure (P) / Saturated Water Vapor Pressure (P0)

RH = P/P0

• Saturated Water Vapor Pressure (P0) depends on the temperature.

### Two states

State 1

• Actual water vapor pressure at beginning = P1
• RH = 80%
• Saturated water vapor pressure at beginning = P10 = 12.171 kPa

State 2

• Actual water vapor pressure at 200C = P2
• RH = 100% (saturated)
• Saturated water vapor pressure at 200C = P20 = 2.302 kPa

### Determine actual water vapor pressure in state 1

• P1 = RH * P10
• P1 = (80 /100)* 12.171
• P1 = 9.737 kPa

### Determine actual water vapor pressure in state 2

• P2 = RH * P20
• P2 = (100/100)* 2.302 = 2.302 kPa
• P2 = 2.302 kPa

### Determine moisture (water vapor) mass in the state 1

Apply PV = mRT for water vapor

P1 = 9.737 kPa

• 9.737 * 103 * 1 = m1 * 461.5 * 323
• m1 = 0.065 kg
• m1 = 65 g

### Determine moisture (water vapor) mass in the state 2

Apply PV = mRT for water vapor

P2 = 2.737 kPa

• 2.737 * 103 * 1 = m2 * 461.5 * 293
• m2 = 0.065 kg
• m2 = 17 g

Condensed water vapor mass = m1 - m2

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

### How relative humidity is maintained by air conditioner.

Air conditioner does the job of removing water vapor when water vapor content is higher than expected level to keep comfortable environment.

### Calculate amount of water to raise RH value

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.

• From current RH value of and required RH values, current water vapor pressure and required water vapor pressure can be calculated.
• Values of current water vapor pressure and required water vapor pressure can be used to current water vapor mass and required water vapor mass in the defined space. (apply PV = mRT twice forcurrent water vapor pressure and required water vapor pressure)
• Take the difference of required water vapor mass and current water vapor mass.

#### How to calculate water vapor in air?

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.

• PV = mRT
• m = PV/RT

• P = Actual water vapor pressure
• V = volume of considering space
• T = temperature in K
• m = Actual water vapor mass
• R = Universal gas constant

#### relative humidity formula vapor pressure?

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.

#### what is saturated air

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 definition

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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