When thermodynamics goes from this..

When thermodynamics goes from this.. Cal Poly Pomona Thermodynamics: Branch of Physics Heat Transfer (Q, Qout) Mechanical Work (W, Wout) Other energy changes due to changes in: Specific Volume, v Internal Energy, u Enthalpy, h Entropy, s -> Temperature -> Pressure -> Volume First Law of Thermodynamics Definition: First Law of Thermodynamics is a fundamental concept in physics that forms the cornerstone of the laws of thermodynamics. It states that energy cannot be created or destroyed, but can only change form. Energy remains constant; it transforms but cannot be created or destroyed. Total Energy Equal To THIS: To THIS: To THIS: To THIS: To THIS: And finally THIS 💔: Problem 3. Consider the fourth order differential equation: y'''' - k^2 y'' = g(x) 1. Find the general solution to the homogeneous equation. 2. Show that a particular solution to Eq. (1) can be written in the form Φp(x) = 1/k^2 ∫ xg(x)dx - x/k^3 ∫ g(x)dx + e^kx/2k^3 ∫ g(x)e^-kx dx - e^-kx/2k^3 ∫ g(x)e^kx dx And that ln Γ(x) = (x - 1/2) ln x - x + 1/2 ln(2π) x > 1 3. Show that the general solution in part (b) can be rewritten in the form Φp(x) = ∫ g(s)G(x-s) ds, where G(ξ) = 1/k^3 (sinh kξ - kξ) 4. Determine the simplest form of the general solution to Eq. (1) in the case g(x) = 1. 1. TURBINES POTENTIAL ENERGY (TEMPERATURE & PRESSURE) (CAN INCLUDE GRAVITATIONAL) MECHANICAL WORK (SHAFT WORK) Turbine Schematic P1 V1 Wout P2 V2 T1 T2 Z (NOT ALWAYS PRESENT) DETAILS OF THIS CONVEN- TION AND MECH WORK -> ELECTRICITY O = dE/dt - Q - W + m_i(h_i + v_i^2/2 + gz_i) - m_e(h_e + v_e^2/2 + gz_e) W = m(h_i - h_e + v_i^2/2 - v_e^2/2 + g(z_i - z_e)) W = m(h_i - h_e) when ΔKE & ΔPE = 0 z = "HEAD" And finally THIS 💔: