(a) Explanation Write the equation of mass balance. m in − m e = Δ m system (I) Here, the inlet mass is m in , the exit mass is m e and the change in mass of the system is Δ m system . The change in mass of the system for the control volume is expressed as, Δ m system = ( m 2 − m 1 ) cv Here, the subscripts 1 and 2 indicates the initial and final states of the system. Consider the given rigid container as the control volume. Initially the cylinder is filled with refrigerant and the valve is in closed position, further no other mass is allowed to enter the cylinder. Hence, the inlet mass is neglected i.e. m in = 0 . Rewrite the Equation (I) as follows. 0 − m e = ( m 2 − m 1 ) cv m e = m 1 − m 2 (II) Write the formula for initial and final volume of refrigerant present in the cylinder. ν 1 = v 1 m 1 (III) ν 2 = v 2 m 2 (IV) Here, the volume is ν , the specific volume is v , the mass is m , and the subscript 1 indicates the initial state, the subscript 2 indicates the final state. Write the energy balance equation. E i n − E o u t = Δ E s y s t e m { [ Q in + W in + m in ( h + ke + pe ) in ] − [ Q e + W e + m e ( h + ke + pe ) e ] } = [ m 2 ( u + ke + pe ) 2 − m 1 ( u + ke + pe ) 1 ] system (V) Here, the heat transfer is Q , the work transfer is W , the enthalpy is h , the internal energy is u , the kinetic energy is ke , the potential energy is pe and the change in net energy of the system is Δ E system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The pressure of 500 kPa is required to move the piston i.e. boundary work required to move the piston. When the valve is opened and refrigerant is withdrawn at the bottom of the cylinder. The boundary work is done on the system. i.e. W in = W b,in , W e = 0 . The heat transfer occurs while refrigerant escapes the cylinder. Neglect the kinetic and potential energy changes i.e. ( Δ ke = Δ pe = 0 ) . The Equation (V) reduced as follows. W b,in − Q e − m e h e = m 2 u 2 − m 1 u 1 Q e = − m 2 u 2 + m 1 u 1 − m e h e + W b,in (VI) Write the formula for boundary work done on the cylinder (b) To determine The heat transfer.

Fundamentals Of Thermal-fluid Sciences In Si Units

5th Edition

ISBN: 9789814720953

Author: Yunus Cengel, Robert Turner, John Cimbala

Publisher: McGraw-Hill Education

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Chapter 6, Problem 166RQ

(a)

To determine

The work done.

(b)

To determine

The heat transfer.

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Chapter 6, Problem 164RQ

Chapter 6, Problem 167RQ

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