Answer to Question #112310 in Mechanical Engineering for John Timothy

Question #112310
Assume a large primary system that consist of a vessel containing warm water in the system with a temperature of 350,001k. An infinitesimal amount of its heat of 1050j is transferred to a secondary system consisting of a room air at a temperature of 350k. Consequently the water temperature drops to 349,999k. What is the entropy generation: A) If the system is cooled in air. B) If the heat removed from the primary system is used to run a cannot engine process and that rejected by the engine is transferred to the secondary system.
Expert's answer

(A) Air temperature is at 350 K, Heat transfer= dQ= 1050 J

Entropy generation,

"S_{gen}= \\Delta S_{sys}+ \\frac{dQ}{T}"

Here, in case of ambient condititon change in entropy will be zero

"S_{gen}=\\frac{1050}{350}=3 \\frac{J}{K}"

(B) As per the second case we know that for carnot heat engine

"\\frac{Q_1}{Q_2}= \\frac{T_1}{T2}"

"\\frac{1050}{Q_2}= \\frac{350.001}{349.999}"

Q2=1049.99 J

and entropy generation

"S_{gen}=\\frac{1049.999}{349.999}= 2.999 J\/K"

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