(a) Explanation Write the expression for the entropy balance in a closed system. S 2 − S 1 = ∫ 1 2 ( δ Q T ) + σ (I) Here, the entropy at state 2 is S 2 , the entropy at state 1 is S 1 , the heat transfer through the boundary of system is δ Q , the absolute temperature of system is T , the entropy generation within the system is σ . Write the expression for entropy change between two states for an ideal gas. S 2 − S 1 = m [ s ° ( T 2 ) − s ° ( T 1 ) − R ln ( p 2 p 1 ) ] (II) Here, the entropy variable depended on temperature T 1 is s ° ( T 1 ) , the entropy variable depended on temperature T 2 is s ° ( T 2 ) , the gas constant is R , the pressure at state 1 is p 1 and the pressure at state 2 is p 2 . For an adiabatic process as there is no heat transfer across the boundary of system, so δ Q = 0 . Substitute 0 for δ Q in Equation (I) S 2 − S 1 = ∫ 1 2 ( 0 T ) + σ = σ Substitute σ for S 2 − S 1 in Equation (II). σ = m [ s ° ( T 2 ) − s ° ( T 1 ) − R ln p 2 p 1 ] (III) Write the expression for energy balance in a system. Δ U + Δ K E + Δ P E = Q − W (IV) Here, the change in internal energy is Δ U , the change in kinetic energy is Δ K E , the change in potential energy is Δ P E , heat supplied to the system is Q and the work done by system is W . Assume that the changes in kinetic and potential energy of the system are negligible. Also assume that there is no heat transfer across the boundary of the system. Write the expression for change in internal energy. Δ U = − m ( u 2 − u 1 ) Here, mass is u 1 , specific internal energy of state 1 is and the specific internal energy of state 2 is u 2 . Substitute 0 for Δ K E , 0 for Δ P E , 0 for Q and − m ( u 2 − u 1 ) for Δ U in Equation (IV). − m ( u 2 − u 1 ) + 0 + 0 = 0 − W − m ( u 2 − u 1 ) = W W m = − ( u 2 − u 1 ) (V) Conclusion: Refer to Table A-22 “Ideal Gas Properties of Air” to obtain values of s ° ( T 1 ) at 300 K as 1 (b) To determine Whether the process can accomplished adiabatically. The work done if process is adiabatic, else the heat flow direction.

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Author: MORAN

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Chapter 6.13, Problem 50P

(a)

To determine

Whether the process can accomplished adiabatically.

The work done if the process is adiabatic, else the heat flow direction.

(b)

To determine

Whether the process can accomplished adiabatically.

The work done if process is adiabatic, else the heat flow direction.

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Chapter 6.13, Problem 49P

Chapter 6.13, Problem 51P

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FUNDAMENTALS OF ENGINEERING THERMODYNAM

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Whether the process can accomplished adiabatically. The work done if the process is adiabatic, else the heat flow direction.