# Specific Heat of Water Vapor

At atmospheric pressure, water turns into steam at a boiling point of 100Â°C. Once it becomes saturated water vapor, which means that all water molecules have been turned into steam, adding heat further will cause its temperature to increase beyond the boiling temperature. At this stage, the relationship between the change in its temperature and the heat added beyond the boiling point is dictated by the specific heat of water vapor.

## Specific Heat Of Steam

Just like any other substance, water can carry thermal energy within its mass. As this energy increases, water undergoes a series of phase changesâ€” solid ice melts to become liquid water, and liquid water evaporates to become water vapor or steam. Hence, steam is simply water in its gaseous phase.

The specific heat of steam is defined as the amount of heat needed to increase the temperature of its unit mass by one degree, as shown in the equation:

Where:

• c = specific heat of steam [J/kg-K or Btu/lb-Â°F]
• Î”Q = amount of heat or change in thermal energy [J or Btu]
• m = mass of steam [kg or lb]
• Î”T = change in temperature [K or Â°F]

However, the specific heat can also be specified in molar units, as shown in the equation:

Where:

• cm = molar heat capacity of steam [J/mol-K or Btu/mol-Â°F]
• n = number of moles of steam [mol]

Note that the molar mass of steam is 0.0180153 kg/mol.

### Specific Heat Of Steam In Different Dimensional Values

The value of the specific heat of water vapor can be expressed in different forms as follows.

#### Specific Heat Of Steam In J/Kg-K

In SI units, the isobaric, or constant pressure, specific heat of steam is equal to 1,864 J/kg-K, while its isochoric, or constant volume, specific heat is equal to 1,402 J/kg-K at 300 K.

#### Specific Heat Of Steam In Btu

In English units, the isobaric specific heat of steam is equal to 0.445 Btu/lb-Â°F, while its isochoric specific heat is equal to 0.335 Btu/lb-Â°F at 300 K.

### Specific Heat Of Steam In Cal/G-Â°C

In calories, the isobaric specific heat of steam is equal to 0.4452 cal/g-Â°C, while its isochoric specific heat is equal to 0.3349 cal/g-Â°C at 300 K.

## Different Forms Of Specific Heat

Depending on system conditions, there can be two values for specific heat:

• Isobaric specific heat (cp) for constant-pressure systems; and
• Isochoric specific heat (cv) for constant-volume, closed systems.

These two are related by the following equations:

• Î³ = adiabatic index or specific heat ratio [unitless]
• Rsteam = material-specific gas constant for steam [kJ/kg-K]

The material-specific gas constant for steam is equal to 0.4615 kJ/kg-K. Note that this is different from the universal gas constant R which is equal to 8.314 J/mol-K. These two are related by the following equation:

Where:

• M = molecular weight of steam [kg/mol]

### Specific Heat Of Steam At Different Temperatures

When assumed as an ideal gas, the specific heat values of steam are independent of temperature. However, as real gases, they will vary with temperature, as shown in the chart below.

As the temperature increases, the specific heat of steam also increases. However, the opposite is true for its adiabatic index (Î³), whose values have been experimentally determined at various temperatures to be as follows:

At 20Â°C:

100Â°C:

200Â°C:

The isobaric specific heat values of steam at different temperatures from 175 K to 6000 K are listed in the table below:

In doing accurate mass and volume flow calculations, the specific heat values of steam should be corrected according to the table above.

### Effect Of Specific Heat On Enthalpy And Internal Energy

The isobaric and isochoric specific heat values can be used to calculate the change in enthalpy and internal energy of steam, respectively, using the following formulas:

Where:

• Î”H = change in enthalpy of steam [J or Btu]
• Î”U = change in internal energy of steam [J or Btu]

Note that the internal energy is the total energy of a system at constant volume, while the enthalpy is its total energy at constant pressure. Hence, at constant pressure, the change in enthalpy is simply the sum of the change in internal energy and work performed, as shown in the equation below:

Where:

• P = constant pressure [Pa or atm]
• Î”V = change in volume of the system [m3]
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