In these turbines, the high-pressure stage receives gas (point 3 at the figure p 3 = 6.7 MPa T 3 = 1190 K (917☌)) from a heat exchanger and exhausts it to another heat exchanger, where the outlet pressure is p 4 = 2.78 MPa (point 4). Since helium behaves almost as an ideal gas, use the ideal gas law to calculate the outlet temperature of the gas ( T 4,is). Example: Isentropic Expansion in Gas Turbine P-V diagram of an isentropic expansion of helium (3 → 4) in a gas turbine.Īssume an isentropic expansion of helium ( 3 → 4) in a gas turbine. For an ideal gas and a polytropic process, the case n = κ corresponds to an isentropic process. On a p-V diagram, the process occurs along a line (called an adiabat) with the equation p = constant / V κ. Note that this ratio κ = c p/c v is a factor in determining the speed of sound in gas and other adiabatic processes. One for constant pressure (c p ) and one for constant volume (c v ). In which κ = c p/c v is the ratio of the specific heats (or heat capacities) for the gas. The isentropic process (a special case of the adiabatic process) can be expressed with the ideal gas law as: In this equation, the symbol R is the universal gas constant that has the same value for all gases-namely, R = 8.31 J/mol K. R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,.According to the ideal gas law, pressure varies linearly with temperature and quantity and inversely with volume. In an ideal gas, molecules have no volume and do not interact. At constant entropy, i.e., in isentropic process, the enthalpy change equals the flow process work done on or by the system:ĭH = Vdp → W = H 2 – H 1 → H 2 – H 1 = C p (T 2 – T 1 ) (for ideal gas) Isentropic Expansion – Isentropic Compression As can be seen, this form of the law simplifies the description of energy transfer. This work, Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e., change in pressure. In this equation, the term Vdp is a flow process work. The first law of thermodynamics in terms of enthalpy:
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