01 part1-ideal-gas

Ideal Gas

S.GunabalanAssociate ProfessorMechanical Engineering DepartmentBharathiyar College of Engineering & TechnologyKaraikal - 609 609.e-Mail : [email protected]

Ideal Gas

• An ideal gas is a theoretical gas or imaginary gas composed of a set of randomly moving, non-interacting point like particles and they obeys the gas law always.

An ideal gas is an imaginary gas that obeys gas law under all conditions

Properties of ideal gas

– The gas particles are so small (Point mass) or nearly zero mass or virtually no volume

– The collision between ideal gases are elastic. i.e. no attractive or repulsive force during collision

Ideal Gas Equation of state

• The functional relationship between P, V & T

• At very low pressure and high temperature, all real gases and vapour approaches ideal gas behavior is called perfect gas.

Real gas

Perfect gas

Ideal gas

Ideal Gas Equation of stateFor perfect gas, the ideal gas equation is

( Molar Volume )

This is to avoid Kg used in mass


mas of gas in Kg

Gas Constant RGas Molar Weight ( M)Kg/Kmol Gas Constant (R )KJ/KgK

Air 28.97 0.287

Nitrogen 28.01 0.297

Oxygen 32 0.260

Hydrogen 2.016 4.124

Helium 4.004 2.077

Carbon dioxide 44.01 0.189

Steam 18.02 0.461

A mole of a substance has a mass numerically equal to the molecular weight of the substance.

• One g mol of oxygen has a mass of 32 g,• 1 kgmol of oxygen has a mass of 32 kg, • 1 kgmol of nitrogen has a mass of 28 kg


( Molar Volume )

= = m3 = Volume (V)

Ideal Gas Equation of stateFor perfect gas, the ideal gas equation is ( Molar Volume )

= = m3 = Volume (V) Specific Volume –(m3 /Kg)Density - Kg/ m3 Molar Volume

specific Volume V – Volume m3

Ideal Gas Equation of state ( Molar Volume )

= = m3 = Volume (V)

Molar Volume specific Volume V – Volume m3

Units of Pressure

• atmospheric pressure (1 Atm.)= 1.013 bar, = 101325 Pascal (Pa = N/m²); = 760 millimeters of mercury absolute

(mmHgA) = 760 Torr (1 Torr = 1 mm HgA)

Units of Volume & Temperature

• Volume– m3

– Liter (L)– CC (Centimeter Cube)

Temperature - always be expressed in Kelvin scaleT = oC + 273

Important Laws of Perfect Gases01)Boyle's LawThe Volume of a given Mass of a Gas varies inversely as its absolute Pressure, provided the moles and Temperature remains constant. 02)Charles's LawThe volume of a given Mass of a Gas varies directly as its absolute Temperature provided the moles and Pressure is kept constant.03)Gay Lussac lawThe Pressure of a given Mass of a Gas varies directly as its absolute Temperature provided the moles and volume is kept constant.04)Avogadro's LawFor a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant

Important Laws of Perfect Gases05) Regnault's Law:- This Law states that "The two specific Heat at constant Pressure (Cp) and specific Heat at constant Volume (Cv) of a Gas do not change with the change of Temperature and pressure”.06) Joule's Law:- This Law states that "The internal Energy of a given quantity of a Gas depends on the Temperature".

Boyle's LawThe Volume of a given Mass of a Gas varies inversely as its absolute Pressure, provided the moles and Temperature remains constant.

𝒑∝𝟏𝒗

Charles's LawThe volume of a given Mass of a Gas varies directly as its absolute Temperature provided the moles and Pressure is kept constant.

𝒗∝𝑻

Gay Lussac lawThe Pressure of a given Mass of a Gas varies directly as its absolute Temperature provided the moles and volume is kept constant.

P

Avogadro's LawFor a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant

V

𝒗∝𝒏

The volume of a g mol of all the gases at the pressure of 1 atm and at 0 is the same and it is equal to 22.4 litres.

If any two gases have the same pressure, volume and temperature then they contain the same number of molecules

Joule effect and Joule's law

• Joule's law– The specific internal energy of an ideal

gas depends on only the temperature of the gas and it is independent of both pressure and volume.

(The internal energy depends only on temperature)

English physicist James Prescott Joule


• Joule's first law (Joule effect ) (Joule's laws of heating)

Expresses the relationship between heat generated (H) in a conductor and current

flow (I), resistance (R), and time (t).



• The magnetostriction effect describes a property of ferromagnetic materials which causes them to change their shape when subjected to a magnetic field.

• Joule first reported observing change in the length of ferromagnetic rods in 1842



• Gough–Joule effect– A stretched piece of rubber contracts when heated

• demonstrating this effect is to suspend a weight on a rubber band sufficient to elongate it at least 50%. When the stretched rubber band is heated up by an infrared lamp, it does not elongate because of thermal expansion, as may be expected, but it retracts and lifts the weight.


Ideal Gas Law Problems

1. you have 10 mol of a gas at 30oC, occupying a container which is 0.5 L in size. What is the pressure of this gas in atmospheres?• Given data• n = 10 mol• T = 30oC• V = 0.5 L• P = ?

Ideal Gas Law ProblemsT = 30oC = 30oC + 273 = 303 KValues of Gas Constant = 0.0827 Substitute the values nowPx 0.5 L = 10 mol x 0.0827 x303KP = 10 mol x 0.0827 x303K / 0.5 LAns is P = ?: P = 501.2 atm

𝑹=𝟖 .𝟑𝟏𝟒𝟒𝟏𝑲𝑱 /𝑲 .𝒎𝒐𝒍𝑲

Ideal Gas Law ProblemsClass Ex: 2. find the volume of 5 mol of gas which is at 350 mm Hg of pressure, and at a temperature of 110 oC.

1 atm = 760 mmHg? atm = 350 mmHg

Note:

The specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density and is an intrinsic property of matter.

Substance Name Density Specific Volume

Kg/m3 m3/Kg

Air 1.2 0.83

Ice 916.7 0.00109

Water (liquid) 1000 0.00100

Salt Water 1030 0.00097

Mercury 13546 0.00007

Note: Molar volume

• The molar volume is the volume occupied by one mole of a substance at a given temperature and pressure.

• It is equal to the molar mass (M) divided by the mass density (ρ).

Specific heat

• The specific heat - the amount of heat required to raise a unit mass of the substance through a unit rise in temperature.

• For gases– At constant pressure

• Cp

– At constant Volume• Cv

This classic relationship between the specific heats of an ideal gas is called Mayer’s equation

Specific heat

• The specific heat - the amount of heat required to raise a unit mass of the substance through a unit rise in temperature.

• The product of mass and specific heat (mCv) is called the heat capacity at constant volume (J/K)

• The latent heat is the amount of heat transfer required to cause a phase change in unit mass of a substance at a constant pressure and temperature

Questions

• What is an ideal gas ?• What is the difference between Universal gas

constant and characteristics gas constant ?

Questions• What is Ideal gas temperature scale ?

– Kelvin suggested that an ideal gas temperature scale could be based on the product PV for an ideal gas as the thermometric property.

– temperature T on this scale be given by

• Fixed points on the ideal gas temperature scale – The lower fixed point is absolute zero, defined as zero kelvin (K) – The upper fixed point is the triple point of water,

• which is the only temperature at which ice, water and water vapour co-exist in equilibrium

• The triple point is defined as 273.16K (= 0.010C). • K (not 0K) is the symbol for the unit of temperature on the ideal

gas scale, the kelvin.

Questions1. Define Ideal gas ?2. Write the properties of Ideal gas ?3. Define Perfect Gas ?4. Write the ideal gas equation of state ?5. Write the Ideal gas equation for a

perfect gas ?6. Define Boyle's Law ?7. Define Charles's Law ?8. Define Gay Lussac law ?9. Define Avogadro's Law ?10. Define Regnault's Law ? 11. Define Joule's Law ?12. Find the volume of a g mol of gas at

1 atm pressure and at 0

13. Define Joule's laws of heating ?14. Define specific volume ?15. Define a mole?16. Define molar volume ?17. Write the mayer`s equation ?18. Define specific heat ?19. Define heat capacity ?20. Define latent heat ?21. What is the ideal gas temperature

scale?22. Define fixed point and give example ?23. Write the relation between density

and specific volume ?

Questions

Gas Molar Weight ( M)Kg/Kmol

Air

Nitrogen

Oxygen

Hydrogen

Helium

Carbon dioxide

Steam

Fill the table

QuestionsFill the table

S.No

Symbol

Name Units Formulae/ Value

1 2 3 4 5 6 V 7 8 T 9 ρ 10 C

Reference• Rajput, R. K. 2010. Engineering thermodynamics. Jones and Bartlett

Publishers, Sudbury, Mass.• Singh, O. 2003. Applied thermodynamics. New Age International (P) Ltd.,

Publishers, New Delhi.• Nag, P. K. 2002. Basic and applied thermodynamics. Tata McGraw-Hill,

New Delhi.• http://pages.towson.edu/ladon/gases.html• http://

rsnr.royalsocietypublishing.org/content/early/2009/10/12/rsnr.2009.0038.full

• http://en.wikipedia.org/

http://rsnr.royalsocietypublishing.org/content/early/2009/10/12/rsnr.2009.0038.full



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01 part1-ideal-gas