PROPERTIES OF GASESPrepared by Engr. JP Timola

IDEAL GASES

• Model for behavior of real gases

• A gas whose absolute pressure, absolute temperature, and specific volume obey the equation of state

IDEAL GASES

• At low pressures and high temperatures, gases can be modeled by a simple equation - the ideal gas equation of state:

• Where = specific volumeR = specific gas constant

p = pressure

T = temperature

p RT

Specific Gas Constant

• The symbol R is called specific gas constant.

• Value depends on the particular gas being considered

• Can be determined by the equation:

RMW

Specific Gas Constant

:

universal gas constant

8.3144 kJ/kmol-K

1.9859 Btu/pmol- R

1545.3 ft-lb/pmol- R

MW = molar mass or molecular weight

R = specific gas constant [kJ/kg-K, Bt

where

mu/lb -°R]

RMW

Molecular Weight

• Amount of substance can also be given in terms of the number of moles

mMW

n

m

m

:

m = mass [kg, lb ]

n = number of moles [kmol, pmol]

MW = molecular weight [kg/kmol, lb /pmol]

where

Alternative Forms of Ideal Gas Law

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p RT

pV nRT

Tp

MW

( )

pV mRT

pV n MW RT

m TpV

MW

where:

V= volume flow rate m = mass flow rate

V = total volume m = mass

p = absolute pressure T = absolute temperature

= density

Gas constants and Specific Heat Values for Several Gases

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kJ/kg-K Btu/lbm-˚R kj/kg-K ft-lbf/lbm-˚R

Air 28.97 1.4 1.0047 0.24 0.287 53.34

Argon 39.95 1.666 0.5208 0.1244 0.2081 38.68

Carbon Dioxide 44.01 1.288 0.844 0.2016 0.1899 35.11

Helium 4.003 1.666 5.1954 1.241 2.077 386.04

Hydrogen 2.016 1.4 14.3136 3.419 4.125 766.54

Methane 16.043 1.321 2.1347 0.5099 0.5183 96.33

Nitrogen 28.06 1.399 1.0399 0.2484 0.2968 55.16

Octane 114.23 1.046 1.6568 0.3952 0.0728 13.5

Oxygen 32 1.395 0.9185 0.2194 0.2598 48.29

Steam 18.016 1.329 1.8646 0.4454 0.4615 85.77

GAScp R

MW k

EXAMPLE 1

• Determine the density and specific volume of air at room conditions. Assume near sea level.

EXAMPLE 2

• The volume of the passenger compartment of an aircraft is 2100 m3 An equipment maintains the air inside the plane at a pressure of 98 kPa and a temperature of 23˚C.

• A)Calculate the mass of air inside the plane

• B) Determine the percent increase in the mass of air if the pressure is increased to 101 kPa and the temperature drops to 20˚C.

EXAMPLE 3

• A worker pressurized a rigid pipe with dry air to check for leaks. The temperature and absolute pressure of air in the pipes were 35˚C and 250 kPa, respectively. After 24 hours, the worker returns and finds out that the absolute pressure drops to 183 kPa, while the air temperature inside the pipe decreases to 21˚C. Has air leaked out of the pipe? If yes, calculate the mass of air that has leaked out through the fittings.

• The pipe has an inside diameter of 30 mm and length of 20 m.

Activity

• Determine the mass of helium at 600 kPa, 40˚C, to fill up a container with a volume of 35 m3.

• A spherical balloon 3.2 m in diameter contains hydrogen at 25˚C and absolute pressure of 100 kPa. Compute the mass of hydrogen in the balloon.

Special Properties for Ideal Gases

1 1

where:

= specific heat at constant pressure [kJ/kg-K, Btu/lb-R]

= specific heat at constant volume [kJ/kg-K, Btu/lb-R]

k = spec

p

p v

v

v p

p

v

cc c R k

c

R kRc c

k k

c

c

ific heat ratio

Example

• For a certain gas, R = 0.277 kJ/kg-K and k = 1.384. Determine cp, cv and MW.

Additional Properties

• Internal energy (U, u)• Sum of the energies of all molecules in a system

• Units: • kJ, Btu, kJ/s, Btu/hr, ft-lbf/s,

• or

• kJ/kg, Btu/lbm

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Additional Properties

• Enthalpy (H,h)• Amount of energy possessed by a thermodynamic system that

can be transferred between the system and its environment

• H = U + pV [kJ, Btu, kJ/s, Btu/hr, ft-lbf/s]• h = u + pʋ [kJ/kg, Btu/lbm]

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Additional Properties

• Entropy (S,s)• Can be defined using the second law of thermodynamics

• Measure of disorder in a system

• Units: • kJ/K, Btu/˚R

• or

• kJ/kg-K, Btu/lbm-˚R

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Real Gases

• Behave like ideal gases at low pressure and at temperature above its critical point

• Ideal gas equation can be modified into:

• Where Z = compressibility factor

p ZRT