[L1] 1 Absolute Work [L2] 1) Definition [L4] - Work accompanied when the boundary of a system changes, Moving Boundary Work. [L4] - Generally refers to work done by expansion. [L2] 2) Calculation [L4] - pdV integration [L4] - Generally Constant Pressure Process (Isobaric) [L5] * Absolute Work (1W2) = ∫pdV = p(V2-V1) = mR(T2-T1) [L5] * Technical Work (Wt) = -∫Vdp = 0 [L5] * Internal Energy Change (du) = mCv(T2-T1) [L5] * Enthalpy Change (dh) = mCp(T2-T1) [L5] * Heat (1q2) dq = du + pdV = dh [L1] 2 Technical Work [L2] 1) Definition [L4] - Shaft work unrelated to volume change. [L4] - Generally refers to work performed when a system compresses (pressure change work). [L2] 2) Calculation [L4] - Vdp integration - Generally Constant Volume Process (Isochoric) [L5] * Absolute Work (1W2) = ∫pdV = 0 [L5] * Technical Work (Wt) = ∫Vdp = V(p2-p1) = mR(T2-T1) [L5] * Internal Energy Change (du) = mCv(T2-T1) [L5] * Enthalpy Change (dh) = mCp(T2-T1) [L5] * Heat (1q2) dq = du - pdV = du [L1] 3 Difference and Features of Absolute Work and Technical Work [L2] 1) Features [L4] - Generally, a closed system (control mass) involves moving boundary work, and an open system (control volume) involves shaft work, but this is not always the case. [L4] - Both types of work can be involved depending on the system. [L5] * Even in an open system device, if volume change occurs, moving boundary work is involved, reflecting both types of work. [L2] 2) Graph [L4] - Absolute Work (Change in Volume): Area of 1-2-a-b [L4] - Technical Work (Change in Pressure): Area of 1-2-A-B [L2] 1) State Changes of Ideal Gas [L4] - Absolute Work (1W2) = ∫pdV [kJ/kg] [L4] - Technical Work (Wt) = - ∫Vdp [kJ/kg] [L4] - Internal Energy Change (du) = Cv(T2-T1) [kJ/kg] [L4] - Enthalpy Change (dh) = Cp(T2-T1) [kJ/kg] [L4] - Heat (1q2) = du + pdV [kJ/kg] [L2] 2) Isothermal Change (=Constant Temperature Process, Sudden Breakage of Diaphragm, Free Expansion) [L4] - Absolute Work (1W2) = ∫pdV = ∫(RT/V)dV [L4] - Technical Work (Wt) = ∫Vdp = ∫(RT/p)dp [L4] - Internal Energy Change (du) = du = CvdT = 0 [L4] - Enthalpy Change (dh) = dh = CpdT = 0 [L4] - Heat (1q2) = ∫dq = 1q2 = Cv∫dT + ∫dW = 1W2 [L2] 3) Adiabatic Change [L4] - Absolute Work (1W2) : dq = du + pdV [L4] 0 = Cv(T2-T1) + 1W2 [L4] - Technical Work (Wt): dq = dh - vdp [L4] 0 = dh + Wt [L4] - Internal Energy Change (du): dq = du + pdV [L4] du = -1W2 [L4] - Enthalpy Change (dh): dq = dh -vdp [L4] 0 = dh + Wt [L4] dh = -Wt [L4] - Heat (1q2) = 0 [L2] 4) Polytropic Change [L4] (T2/T1) = (V1/V2)^(n-1) = (P2/P1)^((n-1)/n) [L4] - Absolute Work (1W2): 1W2 = (R/(n-1))*(T1-T2) [L4] - Technical Work (Wt): Wt = (nR/(n-1))*(T1-T2) [L4] - Internal Energy Change (du): du = CvdT = Cv(T2-T1) [L4] = -(R/(k-1))*(T1-T2) [L4] = -((n-1)/(k-1))*1W2 [L4] - Enthalpy Change (dh): -k*((k-1)/(n-1))*1W2 [L4] - Heat (1q2) = Cn(T2-T1) (Where, Cn = ((n-k)/(n-1))*Cv