Gas vs Steam: Which has more energy?

Gas vs water: Which has more energy depends on KE+ PE of air and water. Let us begin from the molecular level. Let us take air as an example of gas.

Air: Air consists of N2 and O2 gases. Both gases are diatomic and non-polar in nature. All diatomic molecules are linear and characterized by a single parameter which is the bond length or distance between the two atoms. Diatomic nitrogen has a triple bond, diatomic oxygen has a double bond. They have only weak van der Waals intermolecular attraction working between them. The total degrees of freedom of a diatomic molecule in which the molecule carries energy is five [three translational and two rotational]. Each of these modes gets an equal share of the energy of 1/2kBT [K is Boltzmann constant and T is temperature. Thus, the total internal energy in a diatomic molecule= 5/2KBT. The atoms in a molecule can store energy in vibrations and rotations as well as translations. Each way energy can be stored in the molecule is called a degree of freedom. The compressibility factor for air at high temperature is > 1. That is there is a positive deviation from ideal gas laws.

Superheated steam: It is a product of water which is a triatomic polar molecule. Water’s H-bonds break at 100 degc that leaves van der Walls forces to stay as steam gets superheated. Water molecules [ mol weight = 18 against air mol weight 28 g/mol are much smaller. That makes superheated steam more compressible than air [ emptier space/unit volume]. A non-linear triatomic molecule like superheated steam [water] has a total, nine possible degrees of freedom (three translational, three rotational, and three vibrational), but only seven are accessible at lower temperatures. The internal energy of a superheated steam molecule could be anything from 7/2KBT to 9/2KBT. Much more than air. A very conservative estimate is superheated steam has internal energy more than 1.4 times of air. That explains that superheated steam has much more energy than air. This also explains why superheated steam has much more specific heat than air under similar conditions. At 100 bar, 500 degc, the air has about 1.108 kj/kg-k specific heat while superheated steam has about 2.589 kj/kg-k specific heat which is about 2.5 times. Consequently, for the same hot reservoir and cold reservoir dT [Carnot principle], the air has less specific enthalpy dh. (dh = Cp [T hot – T cold]). This needs a gas turbine with much higher dT across hot and cold reservoirs. This has been discussed in more detail later.  

Credit for images: Google

Enthalpy-Entropy diagram for air

Y-axis is specific enthalpy in kj/kg. The X-axis is entropy in kj/kg-k. Red lines are pressure lines in Mpa. The extreme right-side red line stands for 0.001 Mpa and the extreme left side red line stands for 10 Mpa. Black bold almost horizontal lines are temperature lines. There are two important observations emerging from this diagram [1] at a constant temperature as pressure increases, enthalpy remains practically constant while entropy reduces, and [2] at constant pressure as temperature increases, the enthalpy and entropy both increase.

The most important observation is specific enthalpy of air 100 bar/500 degc is only = 795.9 kj/kg

Enthalpy-Entropy diagram for superheated steam

Y-axis [LHS graph] is enthalpy expressed as kj/kg. The X-axis is entropy expressed as kj/kg-k. There are two sets of curved lines in the image. These are well explained what they stand for. The curves rounded upwards are temperature lines expressed as degc. The curves rounded downwards are pressure lines. The image suggests the following: [1] at a constant temperature when pressure increases the enthalpy reduce and also entropy reduces [2] At constant pressure when the temperature is increased enthalpy and entropy both increase. The most important observation is the specific enthalpy of superheated steam at 100 bar/500 degc = 3373.81 kj/kg. 

There is a huge difference in the enthalpy between superheated steam and air. Superheated steam has enthalpy at 100 bar/500 degc more than four times that of air. Air cannot achieve superheated steam’s enthalpy even at 1700 degc and 100 bar. So, air’s enthalpy is a big limitation while delivering mechanical work. The question is why? This is explained below through the compressibility graphs of air and superheated steam.

The LHS images suggest compressibility of air z>1 and compressibility of superheated steam<1. In other words, under similar conditions, superheated steam is more compressible. Steam is the most compressible gas within all gases because water's stable form is liquid. Steam always wants to go back to liquid. The specific volume of air at 100 bar/500dec is 0.023073 m3/kg while superheated steam specific volume is 0.032453 m3/kg which is one and half times more than air. This suggests, under similar temperature and pressure, superheated steam does more work than steam. 

Summary: Air vs Superheated steam comparison

At the molecular level

The internal energy of air = 5/2KT [Both O2 and N2 in air are diatomic molecules]

The internal energy of superheated steam > 7/2KT. The internal energy of superheated steam is at least 1.4 times more than air. [Explained above]

At thermophysical properties level

I have explained each point in the LHS table in my note above. There are two key points for air compared to superheated steam [1] air has less internal energy and [2] it is less compressible. Therefore, under similar pressure-temperature, the air has less enthalpy than steam.

Gas vs Steam turbine:

The efficiency of gas turbine vs steam turbine: Suppose you have a power plant that generates X MW power. This requires the turbine to do a W amount of work. dH = dU + W or W = dH – dU, since the internal energy of air is < superheated steam, a gas cycle will need to produce more dH. Since dH = Cp [T hot – T cold]. Therefore, a gas cycle runs at a much higher temperature than a steam cycle to do the same work W, but there is a limitation because of wear and tear and material failure at high temperatures. The second important point is in a steam cycle all superheat is squeezed out in the condenser under vacuum. Even if you are very efficient and you discharge the cold gas [air] at 1 bar and 50 degc, you still lose about 350 kj/kg heat in a simple gas cycle. That gives you a low efficiency. Therefore the concept of the combined gas cycle has evolved.

Combined gas cycle: A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55-60 %. In the combined cycle, a Heat Recovery Steam Generator (HRSG) captures exhaust heat from the gas turbine that would otherwise escape through the exhaust stack. The HRSG creates steam from the gas turbine exhaust heat and delivers it to the steam turbine. The steam turbine delivers additional electricity. The steam turbine sends its energy to the generator drive shaft, where it is converted into additional electricity. Because gas turbines have low efficiency in simple cycle operation, the output produced by the steam turbine accounts for about half of the combined cycle gas turbine. The overall electrical efficiency of a combined-cycle power system is typically in the range of 50–60%