Gases  Ratios of Specific Heat
Ratios of specific heat for gases with constant pressure and volume processes.
Internal Energy
For an ideal gas the internal energy  u  is a function of temperature. A change in internal energy can be expressed as
du = c_{v} dT (1)
where
du = change in internal energy (kJ/kg)
c_{v} = specific heat for gas in a constant volume process (kJ/kgK)
dT = change in temperature (K)
Specific heat c_{v} varies with temperature but within moderate temperature changes the specific heat  c_{v}  can be regarded as constant.
Enthalpy
For an ideal gas the enthalpy  h  is a function of temperature. Change of enthalpy can be expressed as
dh = c_{p} dT (2)
where
dh = change in enthalpy (kJ/kg)
c_{p}= specific heat for gas in a constant pressure process (kJ/kgK)
Specific heat c_{p} can within moderate temperature changes be regarded as constant.
The enthalpy in a fluid is defined as:
h = u + p / ρ (3)
where
h = enthalpy (kJ/kg)
u = internal energy (kJ/kg)
p = absolute pressure (Pa)
ρ = density (kg/m^{3})
Combining (3) and the Ideal Gas Law:
h = u + R T (4)
where
R = the individual gas constant (kJ/kgK)
Change in enthalpy can be expressed by differentiating (4):
dh = du + R dT (5)
Dividing (5) with dT:
(dh / dT)  (du / dT) = R (6)
Modifying (6) with (1) and (2):
c_{p}  c_{v} = R (7)
The difference c_{p}  c_{v} is constant for an ideal gas.
Ratio of Specific Heat
The Ratio of Specific Heat can be expressed as:
k = c_{p} / c_{v} (8)
where
k = Ratio of Specific Heat
Ratio of Specific Heat for some gases:
Gas  Ratio of Specific Heat  k  
Acetylene  1.30 
Air, Standard  1.40 
Ammonia  1.32 
Argon  1.66 
Benzene  1.12 
Nbutane  1.18 
Isobutane  1.19 
Carbon Dioxide  1.28 
Carbon Disulphide  1.21 
Carbon Monoxide  1.40 
Chlorine  1.33 
Ethane  1.18 
Ethyl alcohol  1.13 
Ethyl chloride  1.19 
Ethylene  1.24 
Helium  1.66 
Nheptane  1.05 
Hexane  1.06 
Hydrochloric acid  1.41 
Hydrogen  1.41 
Hydrogen chloride  1.41 
Hydrogen sulphide  1.32 
Methane  1.32 
Methyl alcohol  1.20 
Methyl butane  1.08 
Methyl chloride  1.20 
Natural Gas (Methane)  1.32 
Nitric oxide  1.40 
Nitrogen  1.40 
Nitrous oxide  1.31 
Noctane  1.05 
Oxygen  1.40 
Npentane  1.08 
Isopentane  1.08 
Propane  1.13 
R11  1.14 
R12  1.14 
R22  1.18 
R114  1.09 
R123  1.10 
R134a  1.20 
Steam (water)  1.33 
Sulphur dioxide  1.26 
Toluene  1.09 
The Ratio of Specific Heat is dimensionless and the value is the same in the SI and the Imperial system of units.
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