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The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory.
For the expansion (or compression) of an ideal gas from an initial volume and pressure to a final volume and pressure at any constant temperature, the change in entropy is given by: Here is the amount of gas (in moles) and is the ideal gas constant.
10 Σεπ 2020 · a. Use equation (2.32) to show that for a sample of monatomic ideal gas with a fixed number of particles, the energy function is \[E(S, V)=E_{0}\left(\frac{V_{0}}{V}\right)^{2 / 3} e^{S / S_{0}},\] where E 0, V 0, and S 0 are constants with the dimensions of energy, volume, and entropy. b. Use the formulas
Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at \(T_h = 600 \, K \, (327^oC) \) to a cold reservoir at \(T_c = 250 \, K \, (-23^oC)\), assuming there is no temperature change in either reservoir.
Note that the change in entropy can be determined between any states by calculating it for a reversible process. Substitute the known value along with their units into the appropriate equation, and obtain numerical solutions complete with units.
The principle of maximum entropy. The entropy of a discrete probability distribution {p ∗ n} is defined as S = − ∑ n p ∗ nlnp ∗ n , where here we take e as the base of the logarithm. The entropy may therefore be regarded as a function of the probability distribution: S = S ({p ∗ n}).
28 Νοε 2021 · In physical chemistry and thermodynamics, one useful entropy formula relates entropy to the internal energy (U) of a system: dU = T dS – p dV. Here, the change in internal energy dU equals absolute temperature T multiplied by the change in entropy minus external pressure p and the change in volume V.
