Guide Card, Part 8

Additional Topic! 

Gas Laws

The main distinguishing property of gases is their uncanny ability to be compressed into smaller and smaller spaces. Gases are also the least complex state of matter. Don't get it wrong, just because they are the simplest doesn't mean that they are not one of the most interesting and useful states of matter.

Boyle's Law

Boyle's Law states the volume of a definite quantity of dry gas is inversely proportional to the pressure, provided the temperature remains constant.

Mathematically Boyle's law can be expressed as P₁V₁ = P₂V₂

• V₁ is the original volume
• V₂ is the new volume
• P₁ is original pressure
• P₂ is the new pressure

Charles's Law

Charles's Law can be stated as the volume occupied by any sample of gas at a constant pressure is directly proportional to the absolute temperature.

V / T =constant

• V is the volume
• T is the absolute temperature (measured in Kelvin)

Charles's Law can be rearranged into two other useful equations.

V₁ / T₁ = V₂ / T₂

• V₁ is the initial volume
• T₁ is the initial temperature
• V₂ is the final volume
• T₂ is the final temperature

V₂ = V₁ (T₂ / T₁)

• V₂ is the final volume
• T₂ is the final temperature
• V₁ is the initial volume
• T₁ is the initial temperature

Important: Charles's Law only works when the pressure is constant.

Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures.

Combined Law

The combined gas law is a combination of Boyle's Law and Charles's Law; hence its name the combined gas law. In the combined gas law, the volume of gas is directly proportional to the absolute temperature and inversely proportional to the pressure.

This can be written as PV / T = constant. Since for a given amount of gas there is a constant then we can write P₁V₁ / T₁ = P₂V₂ / T₂.

• P₁ is the initial pressure
• V₁ is the initial volume
• T₁ is the initial temperature (in Kelvin)
• P₂ is the final pressure
• V₂ is the final volume
• T₂ is the final temperature (in Kelvin)

This equation is useful if you have the current volume, temperature, and pressure of a gas, and if you have two of the three final values of the gas.

Ideal Gas Law

The ideal gas law is a combination of all the gas laws. The ideal gas law can be expressed as PV = nRT.

• P is the pressure in atm
• V is the volume in liters
• n is the number of moles
• R is a constant
• T is the temperature in Kelvin

The constant R is calculated from a theroretical gas called the ideal gas. The most commonly used form of R is .0821 L * atm / (K * mol). This R will allow the units to cancel so the equation will work out.

Dalton's Law of Partial Pressure:  

The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.

Mathematically, this can be represented as:

Pressure_Total = Pressure₁ + Pressure₂ ... Pressure_n

Reference Card

These Sources Are Useful!

* http://www.engineeringtoolbox.com/pressure-d_587.html

* http://hyperphysics.phy-astr.gsu.edu/hbase/press.html 

* http://www.pharmacology2000.com/physics/Chemistry_Physics/gas_law_problems1.htm 

* http://water.me.vccs.edu/pressure2.htm

* http://www.arborsci.com/ArborLabs/PDF_Files/ASLab_9.pdf

Answer Card

Did you get it right?

Activity Card, Part 2:

1.) The partial pressure of the nitrogen is 0.8 atm.

2.) a. P = 101300 + 100/0.65 = 101450 Pa 

      b. W = 101450 * 0.065 = 6590 J 

      c. If the volume doubles while the pressure stays constant, the temperature must also double. 

Assessment Card:

1.) P = 0.983 atm; 747 mm Hg

2.) Partial Pressure = 128.325 torr

Assesment Card

IT'S TIME TO TEST YOUR KNOWLEDGE!

You have now learned so much about PRESSURE. Now, you're up for some test. God Speed!

Questions: 

1. A radio station announcer reports the atmospheric pressure to be 99.6 kPa. What is the pressure in atmospheres? In millimeters of mercury? (Level of Difficulty: Average)

 

2. A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5% CO2, 18.0%O2 and 85.0%Ar by moles. Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (Level of Difficulty: Average)

Enrichment Card

Having Some Problems? 

You might be stumped at the activity, but hey, everyone has the right to learn again, aye?! Now, here is one question about pressure. The answers and explanation are given, for your guidance. So, enjoy learning!

Question: A 70 kg skier is going down a slope oriented 30 above the horizontal. The area of each ski in contact with the snow is 0.13 m2. Determine the pressure that each ski exerts on the snow.

* To find the pressure, you need area and force.

* Calculate the normal force applied on the snow: 

Fn = mg *Cos @ Fn = 70(9.8) * Cos 30 Fn = 594.09N 

* Now calculate the pressure in pascals, based on the formula: 

P = F/A P = 594.09 / 0.13 P = 4,569.95 Pa 

* The pressure exerted is 4,569.95 Pa/4.57 kPa.

Activity Card, Part 2

Now for some serious PROBLEM SOLVING.

  The Activity Card is divided into two parts, the first one is an experiment and the other is pure solving.

Now, to prove what you have learned over the past lessons. Kindly answer the following questions, and see how you have learned so far! 

Questions:
1. A balloon contains 0.1 moles of oxygen and 0.4 moles of nitrogen. If the balloon is at standard temperature and pressure, what is the partial pressure of the nitrogen?

2. A gas in a cylinder occupies a volume of 0.065 m3 at room temperature (T = 293 K). The gas is confined by a piston with a weight of 100 N and an area of 0.65 m2. The pressure above the piston is atmospheric pressure.
(a) What is the pressure of the gas? 

(b) The gas is heated, expanding it and moving the piston up. If the volume occupied by the gas doubles, how much work has the gas done?
(c) What is the final temperature of the gas?

Source: http://www.pharmacology2000.com/physics/Chemistry_Physics/gas_law_problems1.htm               http://water.me.vccs.edu/pressure2.htm

Activity Card, Part 1

Lab Experiments Are FUN!

  The Activity Card is divided into two parts, the first one is an experiment and the other is pure solving.

Cloud Machine

Description: Observe cloud formation when a gas is allowed to expand quickly in volume.

Required Equipments: Pressure Pumper, match, Empty 20oz or half-liter soda bottle
Procedure:

1. Add a little water to a 20-oz. pop bottle.
2. Light a match and blow it out. Hold it inside the mouth of the bottle and let some of the smoke go in the bottle.
3. Put the Pressure Pumper on top of the bottle.
4. Pump the Pressure Pumper 100 times. What is happening to the pressure inside the bottle?
5. Release the pressure by slowly unscrewing the Pressure Pumper. Carefully watch the air inside the bottle. What happens?

 

Additional Questions:
1. What happens to water vapor as it cools?
2. What is the purpose of the smoke?
3. Why does fog form more often in the early morning than any other time?

Source: http://www.arborsci.com/ArborLabs/PDF_Files/ASLab_9.pdf

Guide Card, Part 7

ONLINE WATCHING IS GOOD!

Here are some YouTube Videos that explains further what PRESSURE really is.

http://www.youtube.com/watch?v=PNhzAcLFjQU

http://www.youtube.com/watch?v=anDWU5oYQUc&feature=related

http://www.youtube.com/watch?v=V9WF3iiyWYQ&feature=related

Guide Card, Part 6

Pascal's Principle

Pressure is transmitted undiminished in an enclosed static fluid.

 

Any externally applied pressure is transmitted to all parts of the enclosed fluid, making possible a large multiplication of force (hydraulic press principle). The pressure at the bottom of the jug is equal to the externally applied pressure on the top of the fluid plus the static fluid pressure from the weight of the liquid. 

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/pasc.html#pp

Guide Card, Part 5

Fluid Kinetic Energy

The kinetic energy of a moving fluid is more useful in applications like the Bernoulli equation when it is expressed as kinetic energy per unit volume 

When the kinetic energy is that of fluid under conditions of laminar flow through a tube, one must take into account the velocity profile to evaluate the kinetic energy. Across the cross-section of flow, the kinetic energy must be calculated using the average of the velocity squared , which is not the same as squaring the average velocity. Expressed in terms of the maximum velocity v_m at the center of the flow, the kinetic energy is

 

Fluid Potential Energy

The potential energy of a moving fluid is more useful in applications like the Bernoulli equation when is expressed as potential energy per unit volume 

The energy density of a fluid can be expressed in terms of this potential energy density along with kinetic energy density and fluid pressure.

Guide Card, Part 4

The Pressure Calculation

There are many physical situations where pressure is the most important variable. If you are peeling an apple, then pressure is the key variable: if the knife is sharp, then the area of contact is small and you can peel with less force exerted on the blade. If you must get an injection, then pressure is the most important variable in getting the needle through your skin: it is better to have a sharp needle than a dull one since the smaller area of contact implies that less force is required to push the needle through the skin.

When you deal with the pressure of a liquid at rest, the medium is treated as a continuous distribution of matter. But when you deal with a gas pressure, it must be approached as an average pressure from molecular collisions with the walls.

Pressure in a fluid can be seen to be a measure of energy per unit volume by means of the definition of work. This energy is related to other forms of fluid energy by the Bernoulli equation.

 Source: http://hyperphysics.phy-astr.gsu.edu/hbase/press.html

Guide Card, Part 3

"Pressured" Units

Since 1 Pa is a small pressure unit, the unit hectoPascal (hPa) is widely used, especially in meteorology. The unit kiloPascal (kPa) is commonly used design of technical applications like HVAC systems, piping systems and similar.

• 1 hectoPascal = 100 Pascal = 1 millibar
• 1 kiloPascal = 1000 Pascal

Some Pressure Levels

• 10 Pa - the pressure below 1 mm of water
• 1 kPa - approximately the pressure exerted by a 10 g of mass on a 1 cm² area
• 10 kPa - the pressure below 1 m of water, or the drop in air pressure when moving from sea level to 1000 m elevation
• 10 MPa - nozzle pressure in a "high pressure" washer
• 10 GPa - pressure enough to form diamonds

Some Alternative Units of Pressure

• 1 bar - 100,000 Pa
• 1 millibar - 100 Pa
• 1 atmosphere - 101,325 Pa
• 1 mm Hg - 133 Pa
• 1 inch Hg - 3,386 Pa

A torr (torr) is named after Torricelli and is the pressure produced by a column of mercury 1 mm high - equals to 1 / 760^th of an atmosphere.

• 1 atm = 760 torr = 14.696 psi

Pounds per square inch (psi) was common in U.K. but has now been replaced in almost every country except in the U.S. by the SI units. Since atmospheric pressure is 14.696 psi - a column of air on a area of one square inch area from the Earth's surface to the space - weights 14.696 pounds.

The bar (bar) is common in the industry. One bar is 100,000 Pa, and for most practical purposes can be approximated to one atmosphere even if

1 Bar = 0.9869 atm

There are 1,000 millibar (mbar) in one bar, a unit common in meteorology.

1 millibar = 0.001 bar = 0.750 torr = 100 Pa

Source: http://www.engineeringtoolbox.com/pressure-d_587.html

Guide Card, Part 2

Pressure: What You Need To Know

Figure 2.1. The Different Pressures

Absolute Pressure

The absolute pressure - p_a - is measured relative to the absolute zero pressure - the pressure that would occur at absolute vacuum. All calculation involving the gas laws requires pressure (and temperature) to be in absolute units. 

Absolute Pressure is the sum of the available atmospheric pressure and the gauge pressure in the pumping system

Absolute Pressure (PSIA) = Gauge Pressure + Atmospheric Pressure

Gauge Pressure

A gauge is often used to measure the pressure difference between a system and the surrounding atmosphere. This pressure is often called the gauge pressure and can be expressed as:

p_g = p_s - p_a         (2)

where

p_g = gauge pressure

p_s = system pressure

p_a = atmospheric pressure

Additional Information: http://www.omega.com/prodinfo/pressuregauges.html 

Atmospheric Pressure

Atmospheric pressure is pressure in the surrounding air at - or "close" to - the surface of the earth. The atmospheric pressure vary with temperature and altitude above sea level.

• Altitude and Air Density

The standard atmosphere (symbol: atm) is a unit of pressure and is defined as being equal to 101,325 Pa or 101.325 kPa. 

Pressure varies smoothly from the Earth's surface to the top of the mesosphere. Although the pressure changes with the weather, NASA has averaged the conditions for all parts of the earth year-round. The following is a list of air pressures (as a fraction of one atmosphere) with the corresponding average altitudes.

fraction of 1 atm	average altitude
	(m)	(ft)
1	0	0
3/4	2,750	9,022
1/2	5,486	18,000
1/3	8,376	27,480
1/10	16,132	52,926
1/100	30,901	101,381
1/1,000	48,467	159,013
1/10,000	69,464	227,899
1/100,000	86,282	283,076

Source:http://en.wikipedia.org/wiki/Atmospheric_pressure

Standard Atmospheric Pressure

Standard Atmospheric Pressure (atm) is used as a reference for gas densities and volumes. The Standard Atmospheric Pressure is defined at sea-level at 273^oK (0^oC) and is 1.01325 bar or 101325 Pa (absolute). The temperature of 293^oK (20^oC) is also used.

In imperial units the Standard Atmospheric Pressure is 14.696 psi.

• 1 atm = 1.01325 bar = 101.3 kPa = 14.696 psi (lb_f/in²)= 760 mmHg =10.33 mH₂O = 760 torr = 29.92 inHg = 1013 mbar = 1.0332 kg_f/cm² = 33.90 ftH₂O

Source: http://www.engineeringtoolbox.com/pressure-d_587.html

Guide Card, Part 1

WHAT IS PRESSURE?

Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal, which is a Newton per square meter.

For an object sitting on a surface, the force pressing on the surface is the weight of the object, but in different orientations it might have a different area in contact with the surface and therefore exert a different pressure.

http://hyperphysics.phy-astr.gsu.edu/hbase/press.html 

This picture summarizes the concept about PRESSURE.