Ratio of Specific Heat

The heat capacity of a gas in a constant pressure process - to the heat capacity of a gas in a constant volume process

Internal Energy

For an ideal gas the internal energy - u - is a function of temperature and the change in internal energy can be expressed as

du = c_v dT (1)

where

du = change in internal energy

c_v = specific heat capacity for the gas in a constant volume process

dT = change in temperature

c_v varies with temperature, but within a moderate temperature change the heat capacity - c_v - can be regarded as constant.

• Specific Heat Capacities for Gases

Enthalpy

For an ideal gas the enthalpy - h - is function of temperature and the change in enthalpy can be expressed as

dh = c_p dT (2)

where

dh = change in enthalpy

c_p= specific heat capacity for the gas in a constant pressure process

c_p can within a moderate temperature change be regarded as constant.

• More about Specific Heat Capacities for Gases

The enthalpy in a fluid is defined as:

h = u + p / ρ (3)

where

h = enthalpy

u = internal energy

p = absolute pressure

ρ = density

Combining (3) and the Ideal Gas Law gives:

h = u + R T (4)

where

R = the individual gas constant

The change in enthalpy can be expressed by differentiating (4):

dh = du + R dT (5)

Dividing (5) with dT gives:

(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.

The Ratio of Specific Heats

The Ratio of Specific Heats can be expressed as:

k = c_p / c_v (8)

where

k = the ratio of specific heats

Ratio of Specific Heats for some common gases:

Since the ratio is dimensionless the value is the same in the SI and the imperial system of units.

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