Explanation Show the given Stirling engine cycle on P − v diagram. For the given Stirling engine with air as the working fluid, let v i , T i , P i , and s i be specific volume, temperature, pressure and specific entropy at the i t h state respectively. Write the expression of ideal gas equation for the isothermal process 3-4. P 4 = P 3 v 3 v 4 (I) Write the expression of ideal gas equation for the constant volume process 4-1. T 1 = T 4 ( P 1 P 4 ) (II) Write the expression of heat input to the Stirling engine cycle ( q in ) . q in = R T 1 ln v 2 v 1 (III) Here, gas constant of air is R . Write the expression of heat rejected by the Stirling engine cycle ( q out ) . q out = R T 3 ln v 4 v 3 (IV) Write the expression of entropy change for the process 1-2 of the Stirling cycle ( s 2 − s 1 ) . s 2 − s 1 = c v ln T 2 T 1 + R ln v 2 v 1 (V) Here, specific heat of air at constant volume is c v . Write the expression of exergy loss for the isothermal process 1-2 of the given ideal Stirling engine cycle ( x dest,1-2 ) . x dest,1-2 = T 0 ( s 2 − s 1 − q in T source ) (VI) Here, temperature of the surroundings is T 0 , and the temperature of the heat source is T source . Write the expression of entropy change for the isothermal process 3-4 of the Stirling cycle ( s 4 − s 3 ) . s 4 − s 3 = c v ln T 4 T 3 + R ln v 4 v 3 (VII) Write the expression of exergy loss for the isothermal process 3-4 of the given ideal Stirling engine cycle ( x dest,3-4 ) . x dest,3-4 = T 0 ( s 4 − s 3 + q out T sink ) (VIII) Here, temperature of the sink is T sink . Conclusion: Substitute 50 kPa for P 3 and 12 for ( v 3 v 4 ) in Equation (I). P 4 = ( 50 kPa ) ( 12 ) = 600 kPa Substitute 298 K for T 4 , 3,600 kPa for P 1 , and 600 kPa for P 4 in Equation (II). T 1 = ( 298 K ) ( 3 , 600 kPa 600 kPa ) = 1788 K Substitute 0.287 kJ / kg ⋅ K for R , 1788 K for T 1 , and 12 for v 2 v 1 in Equation (III). q in = ( 0.287 kJ / kg ⋅ K ) ( 1788 K ) ln ( 12 ) = 1 , 275 kJ / kg Substitute 0

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Author: CENGEL

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Chapter 9.12, Problem 141P

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The exergy destruction for each process of Stirling cycle.

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Chapter 9.12, Problem 140P

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