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In the case of an ideal gas, the heat capacity is constant and the ideal gas law PV = nRT gives that α V V = V/T = nR/p, with n the number of moles and R the molar ideal-gas constant. So, the molar entropy of an ideal gas is given by (,) = (,) + . In this expression C P now is the molar heat capacity. The entropy of inhomogeneous ...
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
The measurement, known as entropymetry, [83] is done on a closed system with constant number of particles and constant volume , and it uses the definition of temperature [84] in terms of entropy, while limiting energy exchange to heat ::= (), = The resulting relation describes how entropy changes when a small amount of energy is introduced into ...
Changes in the entropy caused by changes in the external constraints are then given by: = = (/ ) = / = [() ()] / where we have twice used the conservation of probability, Σ dp i = 0 . Now, Σ i d ( E i p i ) is the expectation value of the change in the total energy of the system.
The Sackur–Tetrode constant, written S 0 /R, is equal to S/k B N evaluated at a temperature of T = 1 kelvin, at standard pressure (100 kPa or 101.325 kPa, to be specified), for one mole of an ideal gas composed of particles of mass equal to the atomic mass constant (m u = 1.660 539 068 92 (52) × 10 −27 kg [5]).
while for bimolecular gas reactions A = (e 2 k B T/h) (RT/p) exp(ΔS ‡ /R). In these equations e is the base of natural logarithms, h is the Planck constant, k B is the Boltzmann constant and T the absolute temperature. R′ is the ideal gas constant. The factor is needed because of the pressure dependence of the reaction rate.
The total energy of the system at any value of x is given by the internal energy of the gas plus the potential energy of the weight: = + + where T is temperature, S is entropy, P is pressure, μ is the chemical potential, N is the number of particles in the gas, and the volume has been written as V=Ax.
The physical entropy may be on a "per quantity" basis (h) which is called "intensive" entropy instead of the usual total entropy which is called "extensive" entropy. The "shannons" of a message ( Η ) are its total "extensive" information entropy and is h times the number of bits in the message.