Gas laws.
Gas Laws

One of the most amazing things about gases is that, despite wide differences in chemical properties, all the gases more or less obey the gas laws.  The gas laws deal with how gases behave with respect to pressure, volume, temperature, and amount.

Pressure

Gases are the only state of matter that can be compressed very tightly or expanded to fill a very large space.  Pressure is force per unit area, calculated by dividing the force by the area on which the force acts.  The earth's gravity acts on air molecules to create a force, that of the air pushing on the earth.  This is called atmospheric pressure.

The units of pressure that are used are pascal (Pa), standard atmosphere (atm), and torr.  1 atm is the average pressure at sea level.  It is normally used as a standard unit of pressure.  The SI unit though, is the pascal. 101,325 pascals equals 1 atm.

For laboratory work the atmosphere is very large.  A more convient unit is the torr.  760 torr equals 1 atm.  A torr is the same unit as the mmHg (millimeter of mercury).  It is the pressure that is needed to raise a tube of mercury 1 millimeter.

The Gas Laws: Pressure Volume Temperature Relationships

Boyle's Law:  The Pressure-Volume Law

Robert Boyle (1627-1691)

Boyle's law or the pressure-volume law states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant.

Another way to describing it is saying that their products are constant.

PV = C

When pressure goes up, volume goes down. When volume goes up, pressure goes down. 
From the equation above, this can be derived:

P₁V₁ = P₂V₂ = P₃V₃ etc.

This equation states that the product of the initial volume and pressure is equal to the product of the volume and pressure after a change in one of them under constant temperature.  For example, if the initial volume was 500 mL at a pressure of 760 torr, when the volume is compressed to 450 mL, what is the pressure? 
Plug in the values:

P₁V₁ = P₂V₂

(760 torr)(500 mL) = P₂(450 mL) 
760 torr x 500 mL/450 mL = P₂ 844 torr = P₂ 
The pressure is 844 torr after compression.

Charles' Law:  The Temperature-Volume Law

Jacques Charles (1746 - 1823)

This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature.

V  T

Same as before, a constant can be put in:

V / T = C

As the volume goes up, the temperature also goes up, and vice-versa. 
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

V₁ / T₁ = V₂ / T₂ = V₃ / T₃ etc.

Gay-Lussac's Law:  The Pressure Temperature Law

Joseph Gay-Lussac (1778-1850)

This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.

P  T

Same as before, a constant can be put in:

P / T = C

As the pressure goes up, the temperature also goes up, and vice-versa. 
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

P₁ / T₁ = P₂ / T₂ = P₃ / T₃ etc.

Avogadro's Law:  The Volume Amount Law

Amedeo Avogadro (1776-1856)

Gives the relationship between volume and amount when pressure and temperature are held constant.  Remember amount is measured in moles.  Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract.

If the amount of gas in a container is increased, the volume increases.  If the amount of gas in a container is decreased, the volume decreases.

V  n

As before, a constant can be put in:

V / n = C

This means that the volume-amount fraction will always be the same value if the pressure and temperature remain constant.

V₁ / n₁ = V₂ / n₂ = V₃ / n₃ etc.

The Combined Gas Law

Now we can combine everything we have into one proportion:

The volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure. 
Same as before, a constant can be put in:

PV / T = C

As the pressure goes up, the temperature also goes up, and vice-versa. 
Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.

P₁V₁ / T₁ = P₂V₂ / T₂ = P₃V₃ / T₃ etc.

The Ideal Gas Law

The previous laws all assume that the gas being measured is an ideal gas, a gas that obeys them all exactly.  But over a wide range of temperature, pressure, and volume, real gases deviate slightly from ideal.  Since, according to Avogadro, the same volumes of gas contain the same number of moles, chemists could now determine the formulas of gaseous elements and their formula masses.  The idea gas law is:

PV = nRT

Where n is the number of moles of the number of moles and R is a constant called the universal gas constant and is equal to approximately 0.0821 L-atm / mole-K.

Force and motion:

Definition of a force.
Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

a = F_net / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

F_net = m * a

Net force, forces in equilibrium, F =ma
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Forces and pressure :
Definition of pressure .
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.

Pressure, pressure and depth, calculation of pressure
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Heat :
Definition of specific heat capacity.
Definition: Specific heat capacity is the amount of heat energy required to raise thetemperature of a body per unit of mass.

In SI units, specific heat capacity (symbol: c) is the amount of heat in joules required to raise 1 gram of a substance 1 Kelvin.

Also Known As: specific heat, mass specific heat

Specific heat capacity and calculations.
Specific Heat Capacity (C or S ) - The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity of the substance. The quantity of heat is frequently measured in units of Joules(J). Another property, the specific heat, is the heat capacity of the substance per gram of the substance. The specific heat of water is 4.18 J/g° C

How to Use a Micrometer?
1. Turn the thimble until the object is gripped gently between the anvil and spindle.

2. Turn the ratchet knob until a "click" sound is heard. This is to prevent exerting too much pressure on the object measured.

3. Take the reading.

Zero error in case of screw gauge

While taking a reading, the thimble is turned until the wire is held firmly between the anvil and the spindle.

The least count of the micrometer screw can be calculated using the formula given below:

Least count 

= 0.01 mm

Types of error in micrometer screw gauge reading

Every micrometer prior to its use should be thoroughly checked for backlash error or zero error.

a.Backlash error: Sometimes due to wear and tear of the screw threads, it is observed that reversing the direction of rotation of the thimble, the tip of the screw does not start moving in the opposite direction immediately, but remains stationary for a part of rotation. This is called back lash error.

b.Zero error: If on bringing the flat end of the screw in contact with the stud, the zero mark of the circular scale coincides with the zero mark on base line of the main scale, the instrument is said to be free from zero error. Otherwise an error is said to be there. This can be both positive and negative zero error.

Calculating micrometer screw gauge reading: 
Total observed reading = main scale reading + (circular scale division coinciding the base line of main scale) x least count

True diameter = observed diameter – zero error

Example, main scale reading = 2mm or 0.2cm

Circular scale reading = 56, so 56 x 0.001 = 0.056cm

So observed reading = 0.2 + 0.056 = 0.256cm

Screw-gauge

The screw has a known pitch such as 0.5 mm. Pitch of the screw is the distance moved by the spindle per revolution. Hence in this case, for one revolution of the screw the spindle moves forward or backward 0.5 mm. This movement of the spindle is shown on an engraved linear millimeter scale on the sleeve. On the thimble there is a circular scale which is divided into 50 or 100 equal parts.

When the anvil and spindle end are brought in contact, the edge of the circular scale should be at the zero of the sleeve (linear scale) and the zero of the circular scale should be opposite to the datum line of the sleeve. If the zero is not coinciding with the datum line, there will be a positive or negative zero error as shown in figure below.

Introduction to Physics:
Micrometer screw gauge and zero error
Introduction to micrometer screw gauge reading:

A screw pitch gauge also known as a micrometer is a precision instrument. It is used for measuring diameter of circular objects mostly wires, with an accuracy of 0.001cm. It consists of a hollow cylinder mounted on a U frame. The hollow cylinder leads to a ratchet which is meant for fine adjustment. The U frame consists of a flat end known as stud and a screw on the other side. This screw can be moved inside the nut by fitted in the U frame by rotating the hollow cylinder called the thimble. This is called the main scale. The hollow cylinder or the thimble is graduated into 50 or 100 equal parts. This is called the circular scale.

Micrometer screw-gauge is another instrument used for measuring accurately the diameter of a thin wire or the thickness of a sheet of metal.

It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble.