Explanation Write the expression for gas constant. R = R ¯ M (I). Here, the universal gas constant is R ¯ , Gas constant is R and molecular weight of water is M . Write the expression for mass of gas using ideal gas Equation. m = p 1 V 1 R T 1 (II). Here, mass of the air is m , pressure at state 1 is p 1 , gas constant is R , and volume at state 1 is V 1 and temperature at state 1 is T 1 . Write the expression for temperature at state 2 using ideal gas equation. T 2 = p 2 V 2 m R (III) Write the expression for specific heat at constant volume. C V = R k − 1 (IV) Here, specific heat at constant volume is C v , and specific heat ratio is k . Write the expression for heat transfer. Q = m C V ( T 2 − T 1 ) (V) Here, the heat transfer is Q . Conclusion: Substitute 8.314 kJ / kmol ⋅ K for R ¯ and 39.94 kg / kmol in Equation (I). R = 8.314 kJ / kmol ⋅ K 39.94 kg / kmol = 0.2081 kJ / kg ⋅ K Substitute 2 bar for p 1 , 2 m 3 for V 1 , 0.2081 kJ / kg ⋅ K for R and 50 °C for T 1 in Equation (II). m = ( 2 bar ) ( 2 m 3 ) ( 0.2081 kJ / kg ⋅ K ) ( 50 + 273.15 ) K = ( 2 bar ) ( 100 kPa 1 bar ) ( 2 m 3 ) ( 0.2081 kJ / kg ⋅ K ) ( 323.15 K ) = ( 2 bar ) ( 100 kPa 1 bar ) ( 1 kN / m 2 1 kPa ) ( 2 m 3 ) ( 67.2475 kJ / kg ) ( 1 kN ⋅ m / kg 1 kJ / kg ) ≈ 5.94 kg Substitute 8 bar for p 2 , 2 m 3 for V 1 , 0

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 3.14, Problem 122P

To determine

The final temperature.

The heat transfer.

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Chapter 3.14, Problem 121P

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The final temperature. The heat transfer.