Monday, March 15, 2010

Patent leather highly fashionable leather


The history of patent leather begins in the early 19th century and owes its invention to Seth Boyden of Newark, New Jersey. During the year 1818, Boyden began to investigate the possibility of creating a version of leather that was treated in such a way that the material retained its desirable qualities of protection and durability. At the same time, this new type of leather would also have an appearance that would be decidedly more dressy than work boots and similar leather goods.
Using a formula that was based on a series of treatments using layers of linseed oil based coats, the new shiny leather began commercial production on 20 September 1819. Boyden’s efforts resulted in the production of glossy leather that quickly caught on the perfect compliment for formal dress. Almost two centuries later, patent leather still maintains the status of being part of a formal look for men and women alike.
Patent leather begins life as a superior grade of fine grain leather that undergoes a process to achieve the glossy look that is considered sophisticated. Originally, this was accomplished by applying layers of a linseed oil finish to the leather, gradually creating the sleek appearance. As time went on, the invention of plastics impacted the methods for producing patent leather.
Plastic finishes were able to produce effects similar to the application of several treatments with linseed oil, with the advantage of considerably less monetary investment on the part of the producer. Over time, the development of synthetic resins further simplified the process and cut production costs even further, making the mass production of patent leather possible.
Characterized by a glass like finish that catches the light, the typical patent leather accessory is a solid black. In addition to the mirror like finish, patent leather is also virtually waterproof, while still retaining a very flexible texture. The visual elements of patent leather have made it a sought after material for all sorts of formal accessories. Just about all men’s footwear produced to be worn with tuxedos are patent leather shoes. Many formal types of heels for women are also produced using patent leather. Clutches and small handbags for women are also made using patent leather, as well as some formal wallets and cigarette cases. Essentially, patent leather is always considered an integral part of formal wear.
With almost two centuries of history, patent leather is one type of material that seems to keep going no matter what current fashion trends dictate. It seems that as long as there is a need to dress up for an occasion, patent leather will be found in closets and tuxedo shops across the country.
Patent leather research by B LC leather

Patent leather highly fashion able leather  
BLC Leather Technology Centre present an overview of patent and metallic fashion finishing effects that can be seen on more and more leathers these days. Every few years patent and other highly fashionable finishes applied by foils such as metallic become heavily demanded but often present a range of technical difficulties to the tanner or finisher
Leather is a fashion item subject to the seasonal and annual variations that occur in the fashion industry. As a result, every few years there is a demand on the leather industry to produce patent and metallic leathers. These trends certainly add sparkle to a wardrobe either in the form of shoes, handbags, belts or even full garments.
The potential downside of fashion trends being imposed on a traditional industry such as leather is that new products and effects will invariably have their own unique problems and technical issues. The recent metallic trend has imposed the development of metallic finishes on leather suppliers resulting in an increasing number of technical problems and complaints within the industry.
Patent leathers are also currently highly fashionable, but tanners, retailers and end users need to take care to avoid the many potential problems and issues with the manufacture of this type of leather. It is important to ensure good practice is employed in the coating system used. Patent leathers were traditionally produced in black or white for evening wear and children’s footwear, but increasing fashion trends have led to the production of patent in a myriad of colours. New patent leathers are also being developed to provide two tone, metallic and pull-up patent finishes.

History
During the year 1818, Seth Boyden of Newark, New Jersey, began to investigate the possibility of creating a version of leather that would retain its desirable qualities of protection and durability whilst at the same time having a more dressy appearance.
Originally, this was accomplished by applying layers of a linseed oil finish to fine grain leather, gradually creating the sleek appearance which resulted in the production of glossy leather that was quickly adopted as a complement to formal dress.
Coating with linseed oil required considerable time and effort. Many individual applications were needed with a long drying period for each coat, which meant that it could take up to four weeks of production time. As time went on, the invention of plastics impacted the methods for producing patent leather.
Plastic finishes were able to produce effects similar to the application of several treatments with linseed oil, with the advantage of considerably less monetary investment on the part of the producer. The original methods of production as well as being time consuming also had poor fastness properties. Technology has moved on considerably and genuine patent leathers are produced by a solvent based polyester/isocyanate cross-linking system. There are also water based finishes to produce the same patent ‘wet look’ which are easier to produce with greatly reduced problems and hazards.
The standard method of finishing, which applies to the majority of patent leathers, is outlined in the next section. However, it is also possible to use transfer papers to produce the patent effect. Great care needs to be taken when using these papers, which can either be the ‘whole’ finish including base coats or simply the patent top coat. The papers are applied using a conventional tannery press at 125°C for 3 to 5 seconds at 100 bar pressure.

Standard method of production for patent leathers
Leather preparation

It is the final coat applied that gives the required gloss, but the base coats and leather preparation also have a profound impact on the final properties.
Most patent leathers are produced on corrected grain. Careful preparation is required and the leather needs to have good buffing properties and a tight flat grain. One of the main reasons for the grain correction is that the production of such a high gloss finish needs a surface free from blemishes. The surface is then heavily impregnated, covered with pigment coats prior to the application of the final gloss. Vegetable retannages are used to enhance the deep buffing and often the final surface deposition of an acrylic resin to enhance the tightness. It is also important to ensure that the fatliquors used penetrate to ensure the surface is free from grease.
Dust is a major enemy of patent leathers so it is good practice to spray the flesh side of the leather with a light seal to avoid subsequent cross-contamination.

Finishing system

The finishing sequence comprises of various coats and it is essential that the formulae promote good inter-coat adhesion. The normal sequence is impregnation, base coat, intermediate coat and patent top coat.

Impregnation
The formula needs to be carefully controlled and includes:
  • Impregnating resin of the correct particle size
  • Wetting agent to reduce the surface tension without creating poor wet adhesion
  • Strict control of the balance of the resin to penetrator (typically 10% penetrator by volume).
  • Controlled and consistent deposition of the resin at the grain corium junction (typically between 3-5g/sq ft).

Base coat
This is the main fully pigmented covering coat. Selection of resins is important and must reflect the final properties required in the final leather, such as resistance to cracking and solvents, good ironing properties plus wet and dry adhesion.
Adhesion problems can be minimised by avoiding waxes, oils and silicones. The base coat needs to be applied at levels of between 14-16g/sq ft and is usually applied by several rollercoater applications with an intermediate ironing.

Intermediate coat
On conventional leathers this would be called the top coat. This is a heavy coat of nitrocellulose lacquer which provides a bond between the base coat and the patent top coat, improving adhesion. It is usually applied by spraying. Within this coat it is possible to produce ‘effects’, eg antique, two-tone, tips, by the addition of dyes and pigments.

Patent top coat
The application must be carried out in dust free conditions with up to 20g/sq ft (lower amounts for soft leathers). It is important to ensure that there are no air bubbles in the finish, resulting in the application methods being airless spray or curtain coater. Solvent selection is crucial and any solvents that contain water will give a tendency to bloom. The drying can take longer than 12 hours and it is essential to use an isolated room. The area used must be sealed to prevent airborne dust contamination in the surface finish. The drying is usually 2 hours at 25°C followed by around 10 hours at 50°C. Great care is required in handling the final product to prevent the flesh coming into contact with the grain surface.

What can go wrong?
  • Tacky feel and fingermarking
This is probably caused by insufficient crosslinker in the top coat, resulting in a soft surface. To clean, wipe the whole surface with a cloth impregnated with a silicone-based cleaner.
  • Creasing
This can be caused by the combination of adding a ‘thick’ finish to a thin loose leather. The finish accentuates the looseness problem resulting in creasing.
  • Cloudy dull appearance can be caused if the patent coat is contaminated with water. Consider changing solvents.
  • Air bubbles in the finish. This can be caused either by dirt on the surface prior to the patent top coat or incorrect viscosity of the patent top coat, affecting the flow out.
  • Poor flex resistance. Check the failure to determine which coat has failed. It may be that there is too much crosslinker in the patent coat.
  • Problems with transfer papers. Peeling or lifting due to poor bond with leather. Defects in transfer papers allowing humidity to penetrate and lift the transfer papers.

Production of foiled leathers
There are many types of foils and transfers that can be applied to leathers including:
  • printed effects
  • metallic foils
  • crackle foils
  • multilayer foils
  • lacquer/coated films
  • holographic films etc

The production of metallic foiled leathers can be split into a series of stages which are summarised below.

Pre-application checks
Before the foil is applied the following considerations must be made:
  • The leather should be clean and dry crust (can be dyed) without any type of finish.
  • The leather should be free from dust and with a dry, non-greasy surface. Regular checks at the tannery are recommended.
  • The leather should be flat before application with pleats or folds removed by trimming.
  • The plate of the press should be pre-heated to the required temperature before transfer.
  • The felt in the press should be covered with a sheet of Teflon to improve handing and efficiency.

Application of the adhesive
  • The amount of adhesive applied is important and should only be sufficient to ensure good adhesion without peeling. This may initially require development and the amount applied should be monitored for consistency during production. Too much adhesive can result in the whole film peeling off with the foil, this is particularly likely under wet conditions. Too little adhesive can mean low film strength, resulting in low adhesion and ‘powdering off’ of the foil particles.
  • The adhesive is usually applied by spray although rollercoaters can also be used. The absorption to the surface is important and must be consistent from pack to pack. Unfortunately, a process of trial and error is required to find the optimum amount for each particular type of crust.
  • The choice of adhesive is important and is determined by the type and absorption of the crust. The adhesive is  usually an aqueous polyurethane, which may need diluting slightly for spray application or thickening if applied by rollercoater.
  • Usually the adhesive is dried prior to application so it is tacky. Sometimes the foil is applied without the adhesive being dried (wet application). The best route for individual tanners depends on their leathers, circumstances and preferences. Trials should always be carried out to determine the best method and control checks to be used within the tannery. This is to ensure that processing
conditions are maintained. The conditions of manufacture of the end product should also be taken into account, including processes such as moulding, lasting in shoe manufacture and even shipping. Changes in heat and humidity can affect the adhesion of the leather/ adhesive/ foil bonds.

Transfer
Typically, the foil is cut to the approximate size of the leather ensuring a slight overlap
without too much wastage. The first step is to place a Teflon sheet on the felt and then add the leather followed by the cut piece of foil. The latter two are often assembled in advance and placed into the opening on the hydraulic press. Application temperatures and pressure vary but table 1 shows an example of normal settings.
Post transfer
After the foil has been applied it is advisable to leave the leather to mature for around 4 hours to achieve the best results in terms of adhesion, scuff and gloss. The backing carrier paper from the foil should be removed in one constant movement. Further operations such as staking, milling and ironing can be carried out on the foiled leathers to achieve the required handle.

Common problems

As with other leather types, foiled leathers are subject to their own unique series of problems. Some of these are described here with the potential causes.

Foil peeling
There are several reasons for foil peeling:
  • If the surface of the leather is not correctly prepared, (for example too oily or dusty) the foil may not adhere correctly to the surface
  • Incorrect application of foil, for example too high temperatures or pressure
  • Poorly made foil
  • Foil damage during product manufacture: high temperatures/pressures and solvents from glues
  • High temperature and humidity during transport
  • Leather with too much stretch, which causes the foil to crack when pulled out
  • Cleaning of leather with a product which is not suitable

Damage, during one part of leather or product manufacture can make the foil become more susceptible to damage during subsequent operations. These problems can be observed under magnification as small cracks. This allows moisture (or other contaminants) to penetrate the foil leading to further breakdown and loss of adhesion.
Foil can fail in several ways. Foils are usually an aluminium layer with a coloured coating to produce a gold or silver ‘colour’. Failure can occur between the leather and the foil (caused by one of the reasons above) and the indication for this will be the base leather colour showing. The other area can be the foil itself, where there is failure between the aluminium and coloured coating on the foil, this shows as silver colour with the coloured component being removed.
Foil flaking
Often foils can be ‘rubbed away’ from the leather and this can be caused by failure of the leather/adhesive/foil bond as outlined before. Another potential problem may, however, be related to over finishing (re-finishing) the foil to create fashion effects. It is important that the adhesion properties of the foil are tested to ensure suitability in wear.
In one example observed by BLC a foil had been sprayed with a nitrocellulose top coat followed by a coloured wax coat. The leather was then buffed to allow the silver foil to show through on the raised areas of the leather producing a worn antique look. A final protective nitrocellulose coat was then applied. Finish loss was observed and was caused by a failure in adhesion between the layers of the foil used. The foil was sensitive to the heat and humidity conditions that occurred during the over finishing and this resulted in a deterioration of the finish.
Application of any extra finish to a foil needs caution. It is important to ensure sufficient adhesion between coats to prevent layers from separating. To get good adhesion between layers it is necessary to get penetration of one layer into another. This in itself can cause a problem as migration of water/ humidity and solvent can affect the adhesion bond already in place. If the finish layer being applied to the foil is penetrating, then it may also be causing some damage. This then makes the finish more sensitive to further changes in conditions and more likely to show finish problems.
Conclusion
Fashion demands made on the tanner will always create situations where normal rules and standards are not applied. It is important that the tanner installs rigorous checks in their production processing to ensure that for metallic leathers the bonds between leather/adhesive/ foil are consistent. Once leather is foiled, care needs to be taken in subsequent processing as over-sprays and after treatments can affect the original bonds that have been formed. These problems may not surface until the leathers are subjected to variable heat and humidity situations, such as shipping or shoe manufacture. The tanner needs to implement sufficient safeguards and tests to account for this and BLC can provide advice on the areas of testing that should be considered.
BLC can help to identify the cause of problems experienced in the production of specialised leathers and offer technical advice and support to improve production procedures and ensure that appropriate product performance characteristics are achieved. For further information contact Stuart Booth on stuart@blcleathertech.com or +44 (0) 1604 679956.n

Sunday, March 14, 2010

What is Physics?

Thursday, December 3, 2009

What is Physics?

A typical event studied and described by the science of physics: a magnet levitating above a superconductor demonstrates the Meissner effect.Physics (Greek: physis – φύσις meaning "nature") is a natural science; it is the study of matter[1] and its motion through spacetime and all that derives from these, such as energy and force.[2] More broadly, it is the general analysis of nature, conducted in order to understand how the world and universe behave.[3][4]

Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy.[5] Over the last two millennia, physics had been considered synonymous with philosophy, chemistry, and certain branches of mathematics and biology, but during the Scientific Revolution in the 16th century, it emerged to become a unique modern science in its own right.[6] However, in some subject areas such as in mathematical physics and quantum chemistry, the boundaries of physics remain difficult to distinguish.

Physics is both significant and influential, in part because advances in its understanding have often translated into new technologies, but also because new ideas in physics often resonate with the other sciences, mathematics and philosophy.
Apple iPod touch 32 GB (3rd Generation) NEWEST MODEL

Saturday, December 5, 2009

Chapter 11. HEAT 2ND YEAR PHYSICS COURSE SINDH FULL NOTES


Question: Define heat and its unit. Define temperature what the scale used to measure the temperature are.
Answer.
Heat
Heat is a form of energy which flow from hot body to cold body when they are in thermal contact.
Or heat is a form of energy which is related with the average movement of the molecule.
Unit
Heat is measured in Calorie (Calorie is the name of a scientist)
Definition of calorie
The amount of heat required to raise 1⁰C temperature of 1 gram water. In MKS system the unit of heat is joule 1 calorie =4.2 joule
Temperature
The degree of hotness or coldness of a body is called as temperature.
Unit: the unit of temperature is Kelvin it is measured by the help of thermometer.
There are three scale used to measure the temperature
1. Centigrade scale
On this scale the lower fixed point is at 0⁰C and upper fixed point is at 100⁰C where interval between these two points is divided in 100 equal scales. Each scale measures 1⁰C temperature
⁰C= 5/9 (⁰F -32)
2. Fahrenheit scale
On this scale the lower fixed point is at 32⁰F and upper fixed point is at 212 ⁰F where the interval between these two points is divided in 180 equal scales each scale measures 1⁰F temperature.
⁰F = 9/5 (⁰C +32)
3. Kelvin or absolute scale
On this scale the lower fixed point is at 273 k and upper fixed point is at 373 k where the interval between these points is divided in 100 equal scales each scale measure 1k temperature.
K =⁰C +273
Related problem conversation of temperature at different scale
Problem11.1
A normal body temperature is 98.4⁰F Find its temperature at ⁰C? And at K scale?
Sol. Data Fahrenheit temperature Tf = 98.4 ⁰F
Centigrade temperature Tc =?
Kelvin temperature K =?
We know that
Tc = 5/9 (F-32)
Tc = 5/9 (98.4-32)
Tc =5/9 (66.4)
Tc =36.89⁰C …………..1
K = 273 +⁰C
K = 273+ 36.89
K = 309.89⁰F …………..2
Question: What is thermal expansion explain linear expansion? Or prove that L’ = L (1 +αΔT)
Answer: Thermal expansion
If a body expand by gaining some heat from external source its dimension expands more due to the temperature difference the phenomena is called thermal expansion. The volume of body increases due to increasing movement of its molecule.

Linear expansion
The increase in length of a body due to heat is called as linear expansion for example if the length of a rod increases by supplying heat its expansion is linear expansion.
Explanation
Consider a thin rod of uniform cross section area
At temperature T1 ⁰C its length is L
At temperature T 2⁰C its length become L’
The increase in length ΔL of rod is directly proportional to the initial length of the rod L and to the change in temperature ΔT
Therefore
ΔL ∝ L …………..1 ΔL = L’-L change in length
ΔL ∝ Δ T ………………..2 ΔT= T2- T1 change in temperature
Combining 1 and 2

ΔL ∝ LΔT
ΔL= α LΔT ………….3
Where α is a sign of proportionality constant and is called coefficient of linear expansion it unit is 1/K.
The value of coefficient of linear expansion depend upon the nature of material the rate of expansion is different of different material
From eq. 3
ΔL= α LΔT
L’ - L= α LΔT
L’= L + α LΔT
L’ = L (1+ α ΔT) proved

Related problem
Question:
The length of a steel rod is 0.2 cm at 30⁰C what is its final length at 60⁰C?
Solution:
initial length L = 0.2cm
initial temperature T1 =30 ⁰C
final temperature T2 =60⁰C
value of coefficient of linear expansion α for steel = 11✕10 -6 /⁰C
final length L’ = ?
L’ = L (1+ α ΔT) ΔT= T2- T1 change in temperature
L’ = 0.2 ( 1+ 11✕10 -6✕ (60-30))
L’ = 0.2 ( 1+ 11✕10 -6✕30)
L’ = 0.2 ( 1+330 ✕10 -6)
L’ = 0.2 ✕1.000330
L’ =0.200066 cm the final length of the rod


Question: What is volume expansion prove that V’ = V (1 +βΔT)
Answer.
When the volume of a body increases by gaining heat it is called as volume expansion the body`s length, width and height increases.

Explanation
Consider a body of volume =V
At temperature =T1⁰C
Increasing temperature from T1⁰C
To T2⁰C at temperature T2⁰C volume become V’
The change in volume ΔV of the body is directly proportional to its initial volume V and change in temperature ΔT

ΔV ∝ V ……..1 → ΔV = V’ - V
ΔV ∝ΔT …………2 → ΔT = T2 –T1
Combining 1& 2
ΔV = constant vΔT
ΔV = β vΔT ……..3
where β is the constant of proportionality and is called coefficient of volume expansion its unit is 1/⁰C or 1/K
Coefficient of volume expansion depends upon the nature of material different materials expand at different rate and have different value of β
From 3 we know that
ΔV = β vΔT
V’ - V = β vΔT
V’ = V + β vΔT
V’ = V (1 +β ΔT) proved
Question: What is the Relationship between linear and volume expansion? or
Prove that β = 3α

To find the relation between α and β consider a box of rectangular shape. h
At temperature T1⁰ C its length is = l
Its width = b b
Its height = h l
The volume of the body at T1⁰ C V= l ✕ b ✕ h ……… A
When we increase its temperature from T1⁰ C to T2⁰ C thermal expansion takes place in the body it expands three dimensionally and its length, width and height increases so that its volume become larger
The length increases as l’ = l (1+ α ΔT) ……1 l’ is the final length
Width increases as b’ = b (1+ α ΔT) ……2 b’ is the final width
Height increases as h’=h (1+ α ΔT) …….3 h’ is the final height
Whereas the final volume at temperature T2⁰ C V’= l’ ✕ h’✕ b’ ….4
Putting the value of l’ ✕ h’✕ b’ from 1, 2 and 3 in 4
V’ =l (1+ α ΔT) ✕ h (1+ α ΔT) ✕ b (1+ α ΔT)
V’= l ✕ h✕ b (1+ α ΔT)3 but from A we know that V = l ✕ h✕ b
V’= V (1+ α ΔT)3 …………B
But the final volume expansion of the body(as the coefficient of volume expansion)
V’= V (1+ β ΔT) …………C
Comparing B and C we get
V (1+ β ΔT)= V (1+ α ΔT)3 canceling V from both sides
(1+ α ΔT)3 = 3 α ΔT + 3 α2 ΔT2+ α3 ΔT3
Neglecting the values of α3, α2 because these are the smallest values
(1+ α ΔT)3 = 1+ 3α ΔT
From C we know that (1+ α ΔT)3 = (1+ β ΔT)
(1+ β ΔT)= 1+ 3α ΔT
1- 1+ β ΔT-3α ΔT=0
ΔT (β -3α)=0
β -3α = 0
β = 3α proved


Related problem
An aluminum sphere of radius 0.4 m is heated from 0 ⁰C to 100 ⁰C what will be the change in its volume?
Solution
Radius of sphere r = 0.4m
Initial temperature T1= 0 ⁰C
Final temperature T2 = 100 ⁰C
Change in volume ΔV=?
Coefficient of linear expansion for aluminum α= 24✕ 10-6/⁰C
β = 3α
Therefore coefficient of volume expansion β will be= 3 ✕24✕ 10-6/⁰C
= 72 ✕ 10-6/⁰ Initial volume of the sphere V1= 4/3 π r3
V1= 4/3 π (0.4)3
V1 =0.268m3
Change in volume of sphere ΔV = β v1 ΔT
ΔV = 0.268✕72✕10-6 (100-0)
ΔV = 1.930 ✕10-3
ΔV = 0.00193 m-3
Therefore the change in volume of aluminum sphere is
0.00193 m-3
Uses of thermal expansion
Bimetallic strip
It is made by joining two different metal strip or alloys in length wise outer side is made of that metal which has higher value of linear expansion. Different type of metals expand at different rate (because the value of coefficient of linear expansion α is different for each metal) therefore when this bimetallic is heated one metal expand more than other. These two metals are joint together firmly therefore bimetallic turns in curve shape. The expansion of bimetallic in curve shape is used in different instrument as for temperature control bimetallic thermostat is commonly used. It is used electric iron aircondtionar, refrigerator, room heater, cars radiator fans, oven and fire alarm.

Heat capacity
The amount of heat require to increase the temperature 1 ⁰ C is called heat capacity
C = ΔQ/ ΔT the value of heat capacity depend upon the nature of material and mass greater the mass of material greater will be the heat capacity J/ ⁰ C
Specific heat capacity
The amount of heat require to increase the temperature 1⁰ C of unit mass of a substance is called specific heat capacity.
More heat energy is required to increase the temperature of a substance with high specific heat capacity than one with low specific heat capacity. For instance, eight times the heat energy is required to increase the temperature of an ingot of magnesium as is required for a lead ingot of the same mass. The specific heat of virtually any substance can be measured, including chemical elements, compounds, alloys, solutions, and composites
equations
  • The equation relating heat energy to specific heat capacity, where the unit quantity is in terms of mass is:
where Q is the heat energy put into or taken out of the substance, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
  • Where the unit quantity is in terms of moles, the equation relating heat energy to specific heat capacity (also known as molar heat capacity) is
where Q is the heat energy put into or taken out of the substance, n is the number of moles, c is the specific heat capacity, and ΔT is the change in temperature.

C` = ΔQ/ mΔT
It only depends on the nature of the material not on the mass of the material. Each material has different specific heat capacity. The specific heat capacity of water is 4200j/kg.


Gas laws
Boyle`s law
“The volume of a given mass gas is inversely proportional to its pressure at constant temperature”
P ∝ 1/ V when T = constant
PV = constant T = constant
If the pressure of a gas is increased from P1 to P2 at constant pressure it volume will increase from V1 to V2 then according to Boyle`s law
P1V1 = P2V2
Mass effect: at given temperature pressure of gas P and volume of gas V depend upon mass of gas. Therefore
PV ∝ m
PV/m = constant
P1V1 /m1=P2 V2 /m2 = CONSTANT at temperature constant .

Charles`s law
It states that
“The volume of a given mass gas is directly proportional to its absolute temperature at constant pressure”
V ∝ T when P (pressure)= constant
P/V= CONSTANT when P(pressure)= constant
P1v1 =P2/ T2 at P= CONSTANT


General gas equation
If at constant temperature T1 the pressure of the gas is changed from P1 to P2 so that its volume is changed from V1 to V than according to Boyle’s law
P1 V1 = P2 V
V = P1 V1/ P2 …….A
Now at constant pressure P2 changing its temperature from T1 to T2
Its pressure changed from V to V2 than according to Charles law
V/T1 = V2/T2 …………B
Putting the value of V from equation A in equation B
We have
P1V1/P2 /T1 = V2/T2

P1V1/T1 = P2 V2/T2
PV/T = Constant


Relation between heat capacity and molar heat capacity
Consider M is the molecular weight of a substance the mass of n mole is m
m = nM
Specific heat capacity of the substance
C` = ΔQ/ mΔT
C` = ΔQ/ nMΔT
MC`= ΔQ/ nΔT C = ΔQ/ nΔT
MC` = C