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Unformatted text preview: MAE118A: Introduction to Energy Systems Homework 2 Kowsik Bodi October 20, 2009 Problem a From the second law of thermodynamics, for a reversible process, d s = q T (1) In a Carnot engine, we add heat, q h , to the system at a constant temper ature, T h . Thus the entropy change is, s 1 = q h T h In a later stage, we remove heat, q c , from the system at a constant tem perature, T c so that the system returns to its initial state. The the entropy change in this stage is s 2 = q c T c For an ideal reversible engine, the net entropy change is s 1 + s 2 = 0. In other words, s 2 = s 1 . Thus we have, q h T h = q c T c (2) 1 Problem b We are considering a system where the incoming fluid is of enthalpy h in , and the outgoing fluid is of enthalpy h out . The mass flow rate through the system is constant at m , and pressure, p , is uniform across the system. Heat is being added to the system at the rate Q , and the system is doing work on the environment at the rate W . The work done by the system is of two parts: work done on the sur rounding environment ( W ), and work done against pressure by the fluid in motion ( p d v ). Thus, for a fluid control volume, we have, from the first law of thermodynamics, d E = Q W  p d V (3) Since pressure is uniform, p d V = d ( pV ), d H = Q W (4) For a fluid, enthalpy can be written as, H = mh ( T ). Thus if the fluid composition stays the same across the volume over the time period d t , for a fluid mass of d m , d m ( h out h in ) = Q W (5) Dividing the expression by the time duration to obtain the rate of change, m ( h out h in ) = Q W (6) 2 Problem c: Adiabatic Combustion Tempera ture Adiabatic combustion temperature is the temperature of the products after an exothermic reaction. Assuming a heat release of q , it is defined as the temperature reached by the products due to this heat in a constant pressure process: T = T ad Z T =298 K d h ( T ) = q T = T ad Z T =298 K d TC p ( T ) = q (7) The solution for H 2 is shown here. Methane should be a trivial extension. We know that the heat release per unit mass of the products for the com bustion of H 2 is 3 . 4MJ/kg. We use the following approximations, obtained using curvefits, for the specific heat of the products, H 2 O and N 2 , C p H 2 O / R = 4 . 070 1 . 108 10 3 T + 4 . 152 10 6 T 2 2 . 964...
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 Fall '09
 KowsikBodi
 Thermodynamics, Energy, Heat, Carnot cycle, fuel heating value

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