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Unformatted text preview: Chapter 7 Entropy Entropy Balance 7109 Each member of a family of four take a 5min shower every day. The amount of entropy generated by this family per year is to be determined. Assumptions 1 Steady operating conditions exist. 2 The kinetic and potential energies are negligible. 3 Heat losses from the pipes and the mixing section are negligible and thus . Q 2245 0 4 Showers operate at maximum flow conditions during the entire shower. 5 Each member of the household takes a 5min shower every day. 6 Water is an incompressible substance with constant properties at room temperature. 7 The efficiency of the electric water heater is 100%. Properties The density and specific heat of water at room temperature are ρ = 1 kg/L = 1000 kg/ 3 and C = 4.18 kJ/kg. ° C (Table A3). Analysis The mass flow rate of water at the shower head is m V = = (1 kg / L)(12 L / min) = 12 kg / min ρ The mass balance for the mixing chamber can be expressed in the rate form as m m m m m m m m in out in out = = → = → + = ∆ system (steady) 1 2 3 where the subscript 1 denotes the cold water stream, 2 the hot water stream, and 3 the mixture. The rate of entropy generation during this process can be determined by applying the rate form of the entropy balance on a system that includes the electric water heater and the mixing chamber (the T elbow). Noting that there is no entropy transfer associated with work transfer (electricity) and there is no heat transfer, the entropy balance for this steadyflow system can be expressed as 2 2 1 1 3 3 3 3 2 2 1 1 entropy of change of Rate (steady) system generation entropy of Rate mass and heat by ansfer entropy tr net of Rate free) entropy is work and (since s m s m s m S Q S s m s m s m S S S S gen gen gen out in  = = = + + ∆ = + Noting from mass balance that m m m 1 2 3 + = and s 2 = s 1 since hot water enters the system at the same temperature as the cold water, the rate of entropy generation is determined to be ( ) ( ) ln ( . S m s m m s m s s m C T T gen p = + = = = = 3 3 1 2 1 3 3 1 3 3 1 12 4 495 kg / min)(4.18 kJ / kg.K)ln 42 + 273 15 + 273 kJ / min.K Noting that 4 people take a 5min shower every day, the amount of entropy generated per year is S S t gen gen = = ⋅ ( ) ( ( . ∆ No. of people)(No. of days) kJ / min.K)(5 min / person day)(4 persons)(365 days / year) = (per year) 4 495 32,814 kJ / K Discussion The value above represents the entropy generated within the water heater and the Telbow in the absence of any heat losses. It does not include the entropy generated as the shower water at 42 ° C is discarded or cooled to the outdoor temperature. Also, an entropy balance on the mixing chamber alone (hot water entering at 55 ° C instead of 15 ° C) will exclude the entropy generated within the water heater....
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This homework help was uploaded on 04/18/2008 for the course EML 3007 taught by Professor Chung during the Spring '08 term at University of Florida.
 Spring '08
 Chung

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