Explanation Write the expression for the mass balance for the mixing chamber which acts as a system. m ˙ in − m ˙ out = Δ m ˙ system (I) Here, mass flow rate of the fluid entering the system is m ˙ in , mass flow rate of the fluid leaving the system is m ˙ out and change in mass flow rate of the system is Δ m ˙ system . For steady state, the change in mass flow rate of the system is zero. Δ m ˙ system = 0 Substitute 0 for Δ m ˙ system in Equation (I). m ˙ in − m ˙ out = 0 m ˙ in = m ˙ out m ˙ 1 + m ˙ 2 = m ˙ 3 Here, mass flow rate of the cold water stream is m ˙ 1 , mass flow rate of the hot water stream is m ˙ 2 and mass flow rate of the mixture is m ˙ 3 . Write the formula to calculate mass flow rate of the water at the shower head ( m ˙ ) . m ˙ = ρ V ˙ (II) Here, density of the water is ρ and volumetric flow rate of the water is V ˙ . For the closed system, write the simplified rate form of the entropy balance on the extended system which includes water and its immediate surroundings. S ˙ in − S ˙ out + S ˙ gen = Δ S ˙ system (III) Here, rate of entropy generation is S ˙ gen , rate of change of entropy of the system is Δ S ˙ system , rate of entropy at inlet condition is S ˙ in and rate of entropy at outlet condition is S ˙ out . For steady state, the rate of change of entropy of the system is zero. Δ S ˙ system = 0 Substitute 0 for Δ S ˙ system in Equation (III). S ˙ in − S ˙ out + S ˙ gen = 0 m ˙ 1 s 1 + m ˙ 2 s 2 − m ˙ 3 s 3 + S ˙ gen = 0 S ˙ gen = m ˙ 3 s 3 − m ˙ 1 s 1 − m ˙ 2 s 2 = m ˙ 3 s 3 − ( m ˙ 1 + m ˙ 2 ) s 1 [ ∵ s 1 = s 2 ] = m ˙ 3 s 3 − m ˙ 3 s 1 = m ˙ 3 ( s 3 − s 1 ) = m ˙ 3 c p ln T 3 T 1 (IV) Here, entropies of the water at states 1, 2 and 3 are s 1 , s 2 and s 2 respectively, specific heat capacity of water is c p and temperature of the water at state 1 and 3 are T 1 and T 3 respectively. Write the formula to calculate entropy generation ( S gen ) . S gen = S ˙ gen ( Δ t ) n p n d (V) Here, time taken by each person to take shower is Δ t , number of person is n p and number of days is n d

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 8.8, Problem 79P

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The amount of exergy destroyed by the family per year.

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Chapter 8.8, Problem 78P

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The amount of exergy destroyed by the family per year.

Solution Summary: The author calculates the amount of exergy destroyed by the family per year. The mass balance for the mixing chamber acts as a system.

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The amount of exergy destroyed by the family per year.

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