Explanation Write the expression for 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 the system is Δ E s y s t e m . Substitute Q i n for E i n , W b , o u t for E o u t and Δ U for Δ E s y s t e m . Q i n − W b , o u t = Δ U . (II) Here, boundary work done output is W b , o u t , amount of heat transfer into the system is Q i n and change in internal energy is Δ U . Substitute m c v ( u 2 − u 1 ) for Δ U in Equation (1). Q i n − W b , o u t = m c v ( u 2 − u 1 ) ≅ m c v ( T 3 − T 1 ) . (III) Here, mass of system is m , specific heat at constant volume is c v , internal energy at initial state is u 1 , internal energy at final state is u 2 , initial temperature is T 1 and final temperature is T 2 . Write the expression for the final temperature ( T 2 ) of air in the piston cylinder. P 2 V T 2 = P 1 V T 1 T 2 = P 2 T 1 P 1 . (IV) Here, initial temperature is T 1 , final temperature is T 2 , initial pressure is P 1 and total volume is V . Write the expression for the mass ( m a i r ) of air inside the room. m = P 1 V R T 1 . (V) Here, gas constant is R , initial pressure is P 1 , volume of tank is V and initial temperature is T 1 . Write the expression for the boundary work done output during quasi equilibrium process 2-3. W b , o u t = P 2 ( V 3 − V 2 ) = P 2 V 3 − P 2 V 2 = m R T 3 − m R T 2 W b , o u t = m R ( T 3 − T 2 ) . (VI) Here, mass of nitrogen gas inside the cylinder is m , gas constant is R , initial temperature is T 2 and final temperature is T 3 . Conclusion: Substitute 296 K for T 1 , 200 kPa for P 2 and 100 kPa for P 1 in equation (IV)

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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A substance with fixed chemical composition throughout is called a pure substance like water, air, and nitrogen. A pure substance does not have to be a single element or compound. A mixture of two or more phases of a pure substance is also a pure substan…

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Chapter 4.5, Problem 76P

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