Explanation Write the energy balance equation for closed system. E i n − E o u t = Δ E s y s t e m (I) Here, energy transfer in to the system is E i n , energy transfer from the system is E o u t and change in internal energy of system is Δ E s y s t e m . Substitute W b , i n for E i n , Q o u t for E o u t and Δ U for Δ E s y s t e m in Equation (I). W b , i n − Q o u t = Δ U . (II) Here, boundary work done input is W b , i n , amount of heat transfer exit from the system is Q o u t and change in internal energy is Δ U . Substitute m c v ( T 2 − T 1 ) for Δ U in Equation (II). W b , i n − Q o u t = m c v ( T 2 − T 1 ) . (III) Here, mass of system is m , specific heat at constant volume is c v , initial temperature is T 1 and final temperature is T 2 . Write the final pressure ( P 2 ) of nitrogen gas inside the cylinder. P 2 V 2 1.3 = P 1 V 1 1.3 P 2 = P 1 ( V 1 V 2 ) 1.3 (IV) Here, initial pressure is P 1 and initial volume is V 1 and final volume is V 2 . Write the final temperature ( T 2 ) of oxygen in the tank. P 2 V 2 T 2 = P 1 V 1 T 1 T 2 = P 2 V 2 T 1 P 1 V 1 (V) Here, initial temperature is T 1 , final temperature is T 2 and initial pressure is P 1 . Write the boundary work done input for polytrophic process. W b , i n = − ∫ 1 2 P d V (VI) Here, pressure inside the cylinder is P . Integrate the Equation (VI). W b , i n = − [ P V 1 − n ] 1 2 = − P 2 V 2 − P 1 V 1 1 − n (VII) Here, polytrophic constant is n , initial volume of piston cylinder is V 1 , final volume of piston cylinder is V 2 , initial pressure inside the cylinder is P 1 and final pressure inside the cylinder is P 2 . Substitute m R T 1 for P 1 V 1 and m R T 2 for P 2 V 2 in Equation (VII)

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ISBN: 8220102809444

Author: CENGEL

Publisher: YUZU

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Chapter 4.5, Problem 72P

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The boundary work done input for polytrophic process.

The amount of heat transfer exit from the cylinder.

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Chapter 4.5, Problem 71P

Chapter 4.5, Problem 74P

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The boundary work done input for polytrophic process. The amount of heat transfer exit from the cylinder.