The Gas Laws

The pressure, volume and temperature of a gas all affect one another. This would make the results of an experiment to investigate changes in all three at once complicated to understand. This problem is overcome by making one of them stay constant, whilst the relationship between the other two is investigated.

Boyle’s Law- Volume and Pressure

This Law is about the variation of (a fixed mass of gas) volume with the pressure of a gas at steady temperature. The apparatus shown in the diagrams below may be used to find how the volume of a fixed mass of gas varies with pressure at a constant room temperature.

A syringe can be compressed to increase the pressure which is measured using a pressure sensor. The fixed mass of gas, usually air is trapped in the syringe, and its volume read from the scale.

Alternatively a foot or bicycle pupil is used to increase the pressure which is measured on the Bourdon Gauge. The fixed mass of air is trapped in the capillary tube by a bead of mercury, and its volume measured on the scale.

How Pressure is related to volume for a constant mass and temperature of gas.

Pressure (kPa)100111125143167250
volume of air column(cm 3 )504540353020
Use the results to show a relationship

It is found that when the pressure in increased the volume of the gas decreased so that:

pressure × volume = constant

p × V = k

Boyle’s Law states that: For a fixed mass of gas at constant temperature the pressure is inversely proportional to the volume. i.e. the pressure multiplied by the volume stays constant, provided the temperature does not change.

Kinetic theory of Boyle’s law

The pressure of a gas is caused by the molecules hitting the walls of the container. Reducing the volume results in a shorter distance between the walls and so the number of molecules hitting the walls increases- resulting in increased pressure.

The Pressure Law (Gay Lussac Law)

This law looks at the variation of pressure with temperature at constant volume. The apparatus shown below may be used to find how a fixed mass of gas, at constant volume varies with temperature.

The air is contained in a round bottom flask, which has a constant volume, and the pressure is measured using the pressure sensor attached to the flask by a short tube. It is important to have a short tube so that the temperature in the whole system is equal at any point. The round bottom flask is placed in a water bath which is used to vary the temperature of the water, and hence the air in the flask. Recent results have shown that the thermometer is best placed in the water bath as this gives more accurate results for the temperature of the air in the flask. Placing the thermometer in the flask usually results in a time delay in measuring the temperature of the air inside the flask. The flask should be fully immersed in the water, to ensure all the air in the flask is at the same temperature The temperature must be recorded as Absolute Temperature (in Kelvin) to find a relationship.

The pressure increases proportionally with the absolute temperature (i.e if you double the absolute temperature you will double the pressure provided the mass and volume remain constant). This can be expressed as:

The pressure law states that: For a fixed mass of gas at constant volume the pressure is proportional to the absolute temperature. i.e. the pressure divided by the temperaturee stays constant, provided the volume does not change.

Kinetic theory of Pressure law

If the absolute temperature of a gas increases, the speed of the molecules increases. The force and frequency of the impacts on the walls of the container increases, as this is the cause of pressure,then pressure increases.

How Temperature is related to Pressure for a constant mass and volume of gas.

Temperature ( o C)0205080100
Pressure (kPa)93100110120127
Use this to show a relationship!

Charles’ Law

This is about the variation of volume with temperature at constant pressure. The apparatus shown is used to find how the volume of air varies with temperature provided the pressure remains constant.

The pressure remains constant, since it is equal to the atmospheric pressure plus the small additional pressure due to the weight of the mercury bead on to of the trapped air. This is because the capillary tube is open at one end. The volume of air is measured on the scale and the water bath is used to vary the temperature. The absolute temperature must be used to find a relationship between pressure and volume.

It is found that the volume of the gas increases proportionally with the absolute temperature provided the pressure and mass remain constant. This can be expressed as:

Charles’ Law states that: For a fixed mass of gas at constant pressure the volumee is proportional to the absolute temperature. i.e. the volume divided by the temperature stays constant, provided the pressuree does not change.

 Kinetic theory of Charles’ law

The pressure of a gas is caused by the molecules hitting the walls of the container. If the absolute temperature of the gas increases the speed of the molecules increases. This would result in more forceful and frequent collisions on the walls. However, to maintain the pressure then there must be no increase in the frequency and magnitude of the collisions, so the volume must increase.

How Temperature is related to volume for a constant mass and pressure of gas.

Temperature ( o C)020406080100
Length of air Column(cm)2021.522.924.425.927.3
Proportional to volume
Use these figures to show a relationship!

 The General Gas Law

The three separate gas laws can be summarised by one equation, known as the General Gas Equation:

This is often written as:

Where p1, V1 and T1 refer to one set of conditions of pressure volume and temperature, and p2, V2 and T2 to another set of conditions for the same mass of the same gas.

An individual gas law can be found from this equation by covering up the variable which is kept constant (or cancelling out the variable as it remains constant).

gas law results docx

gas law result pdf

Complete the three graphs above and for two of them try to work out the equation for the straight line, i.e. what is y = mx + c

Pascal

The unit of pressure is the Pascal. I Pa is 1 Nm-2. You must remember you will not measure zero pressure as we have an atmosphere. I atmosphere is the pressure exerted due to our atmosphere and is approximately equal to 1 x105 Pa. This is equivalent to a weight of 105 N acting on a square of area 1m2. At ground level this is approximately the mass of 104 kg on a square metre which equates to about 10 Fiat 500 in 1m2.

Questions

  1. A mass of gas at a pressure of 20kPa has a volume of 3m3. What will be the volume if the pressure is doubled but the temperature remains constant?
  2. The volume of mass of a gas is reduced from 5m3 to 2m3. If the pressure was initially 40 Pa, what will be the new pressure if the temperature remains constant?
  3. The pressure of a fixed volume of gas at 300 K is increased from 5 Pa to 10 Pa, what will the new temperature be?
  4. If pressure of a fixed volume of gas at 200 K is 50 Pa. What would be the pressure if the temperature is increased to 300 K?
  5. The temperature of 6 m3 of gas is increased from 300 K to 400 K. What will be the new volume of the gas if the pressure remains constant?
  6. The volume of a gas is increased from 10 m3 to 20 m3 at constant pressure. Calculate the new temperature if the initial temperature was 300 K.
  7. A mass of gas has a volume of 5 m3, a pressure of 20 Pa and a temperature of 300 K. What will be the new pressure if the volume is changed to 4m3 and the temperature to 400 K?

Answers

  1. 1.5 m3,
  2. 100 Pa
  3. 600 K
  4. 75 Pa
  5. 8 m3
  6. 600 K
  7. 33 Pa
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May 2019

 


Voltage

gills-book

Many teachers think that voltage is too difficult a concept for S1 students to understand. By the time students get to AH we expect them to be fully knowledgeable about voltage, but we don’t clearly explain it to them as we go along. I am as guilty as the next person of doing this so… . My new mission is to teach voltage as best and as fully as I can to S1 and build on the concept each year so that by AH they will feel confident about this work.

Having met Gill Arbuthnott at the Edinburgh International Book Festival (see post in Blog) I was really impressed with the way she tries to explain difficult concepts early on. She has given me permission to reproduce her page 16 on The Volt here.

The Volt

This was named after Alessandro Volta It is a unit of measurement in electricity. It tells us how much energy an electric charge has. You sometimes hear people saying things like, “The number of volts running through the circuit is…”. This doesn’t actually make sense! It’s like saying, “The height running through the mountain is 1000 metres.” Heights don’t run, and neither do volts. There is no Usain Volt!

What is a volt?

So what is a volt? Imagine you are in a building with stairs and a lift. You carry a tennis ball up one floor in the lift, and let it roll back to ground level down the stairs. A battery is like the lift – it’s a way of giving energy to something. In the building this is the ball – in electrical terms it’s an electron.

The ball rolling down the stairs is losing energy. In our circuit the equivalent is the electrons losing their energy to power a bulb. The voltage is equivalent to the height you take the ball up in the lift – more height is equivalent to greater voltage. And the distance the ball goes up in the lift must be the same as the distance it comes down by the stairs.

There are plenty of pictures in the book, but I didn’t think it was as easy to reproduce them. The book is full of more really interesting stuff, and even material about coins that Mr Chemistry opposite Mrs Physics didn’t know about (but then he’s far too young!)

http://www.bloomsbury.com/uk/a-beginners-guide-to-electricity-and-magnetism-9781472915740/

Definition: Potential difference is the amount of work done to move an electric charge from one point to another.

or

Definition: The definition of voltage is the electromotive force or the electrical potential difference between two points in a circuit expressed in volts.

Voltage is a scalar quantity. The SI unit of voltage is the volt, such that 1 volt = 1 joule/coulomb.

The easiest way to understand voltage is to use a water analogy. Using a hose as an example, think of voltage as the amount of pressure forcing water through a garden hose. The higher the pressure in the pipe the more water is forced through the pipe each second. The greater the voltage, the greater the flow of electrical current (that is, the quantity of charge carriers that pass a fixed point per unit of time Q=It) through a conducting or semiconducting medium for a given resistance to the flow.

One volt will drive one coulomb (6.24 × 10 18 ) charge carriers, electrons, through a resistance of one ohm in one second.

Voltage can be direct or alternating. A direct voltage maintains the same polarity at all times. So charges always flow in one direction. In an alternating voltage, the polarity reverses direction periodically. The number of complete cycles per second is the frequency, which is measured in hertz (one cycle per second). An example of direct voltage is the potential difference between the terminals of a cell. Alternating voltage exists between the mains positive and negative.

 

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