CHAPTER7_SECTION4 - Chapter 7 Entropy Entropy Balance 7-109...

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Unformatted text preview: Chapter 7 Entropy Entropy Balance 7-109 Each member of a family of four take a 5-min 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 5-min 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 A-3). 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 steady-flow 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 5-min 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 T-elbow 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.

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CHAPTER7_SECTION4 - Chapter 7 Entropy Entropy Balance 7-109...

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