Applications To Thermodynamic Processes
The table below essentially simplifies the ideal gas equation for a particular processes, thus making this equation easier to solve using numerical methods.
A thermodynamic process is defined as a system that moves from state 1 to state 2, where the state number is denoted by subscript. As shown in the first column of the table, basic thermodynamic processes are defined such that one of the gas properties (P, V, T, or S) is constant throughout the process.
For a given thermodynamics process, in order to specify the extent of a particular process, one of the properties ratios (listed under the column labeled "known ratio") must be specified (either directly or indirectly). Also, the property for which the ratio is known must be distinct from the property held constant in the previous column (otherwise the ratio would be unity, and not enough information would be available to simplify the gas law equation).
In the final three columns, the properties (P, V, or T) at state 2 can be calculated from the properties at state 1 using the equations listed.
Process | Constant | Known ratio | P2 | V2 | T2 |
---|---|---|---|---|---|
Isobaric process |
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P2 = P1 | V2 = V1(V2/V1) | T2 = T1(V2/V1) |
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P2 = P1 | V2 = V1(T2/T1) | T2 = T1(T2/T1) | ||
Isochoric process |
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P2 = P1(P2/P1) | V2 = V1 | T2 = T1(P2/P1) |
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P2 = P1(T2/T1) | V2 = V1 | T2 = T1(T2/T1) | ||
Isothermal process |
|
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P2 = P1(P2/P1) | V2 = V1/(P2/P1) | T2 = T1 |
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P2 = P1/(V2/V1) | V2 = V1(V2/V1) | T2 = T1 | ||
Isentropic process (Reversible adiabatic process) |
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P2 = P1(P2/P1) | V2 = V1(P2/P1)(−1/γ) | T2 = T1(P2/P1)(1 − 1/γ) |
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P2 = P1(V2/V1)−γ | V2 = V1(V2/V1) | T2 = T1(V2/V1)(1 − γ) | ||
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P2 = P1(T2/T1)γ/(γ − 1) | V2 = V1(T2/T1)1/(1 − γ) | T2 = T1(T2/T1) | ||
Polytropic process |
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P2 = P1(P2/P1) | V2 = V1(P2/P1)(-1/n) | T2 = T1(P2/P1)(1 - 1/n) |
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P2 = P1(V2/V1)−n | V2 = V1(V2/V1) | T2 = T1(V2/V1)(1−n) | ||
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P2 = P1(T2/T1)n/(n − 1) | V2 = V1(T2/T1)1/(1 − n) | T2 = T1(T2/T1) |
^ a. In an isentropic process, system entropy (S) is constant. Under these conditions, P1 V1γ = P2 V2γ, where γ is defined as the heat capacity ratio, which is constant for an ideal gas. The value used for γ is typically 1.4 for diatomic gases like nitrogen (N2) and oxygen (O2), (and air, which is 99% diatomic). Also γ is typically 1.6 for monatomic gases like the noble gases helium (He), and argon (Ar). In internal combustion engines γ varies between 1.35 and 1.15, depending on constitution gases and temperature.
Read more about this topic: Ideal Gas Law
Famous quotes containing the word processes:
“It has become a peoples war, and peoples of all sorts and races, of every degree of power and variety of fortune, are involved in its sweeping processes of change and settlement.”
—Woodrow Wilson (18561924)