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Chapter: Mechanical - Engineering Thermodynamics - The Second Law of Thermodynamics

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Solved Problems: Entropy

Mechanical - Engineering Thermodynamics - The Second Law of Thermodynamics


Solved Problems

 

Prob : 5.1 A body at 200oC undergoes an reversible isothermal process. The heat energy removed in the process is 7875 J. Determine the change in the entropy of the body.


 


Comment :  Entropy decreases as heat is removed from the system.

 



Prob : 5.2             A mass of 5 kg of liquid water is cooled from 100oC to 20oC. Determine the change in entropy.        

System                 :         Closed system     

 

Comment            :  Entropy decreases as heat is removed from the system.

 


Prob : 5.3 Air is compressed isothermally from 100 kPa to 800 kPa. Determine the change in specific entropy of the air.

 

System  :  Closed/Open

 

Known  :  p1  =100 kPa

 

p2  =800 kPa

 

To find :  DS - change in Specific entropy

 

Analysis    :   DS   = -R ln  [Since the process is isothermal]

 

0 .287- x ln

 

 =  0.597 -kJ/kgK.

 

Prob : 5.4 A mass of 5 kg of air is compressed from 90 kPa, 32oC to 600 kPa in a polytropic process, pV1.3=constant. Determine the change entropy.

 

System  :  Closed / Open

 

Known  :  p1  =90 kPa

 

T1 =32o=305 K

 

p2  =600 kPa

 

 = kg

 

Process :  pV1.3 =Constant

 

To find :  DS - Change in entropy

 

Analysis      :    S2  -S1  =m

 

Where T2  =T1

 

 =305

 

=473 K

 

\ S2  -S1  = 

 

=-0.517 kJ/K.

 

 

Comment  :   For air the ratio of Cp and Cv is equal to 1.4. Therefore the polytropic index  n -1.3(<1.4) indicates that some heat is removed from the system resulting in negative entropy.

Prob : 5.5 A rigid insulated container holds 5 kg of an ideal gas. The gas is stirred so that its state changes from 5 kPa and 300 K to 15 kPa. Assuming Cp =1.0 kJ/kgK and g =1.4, determine the change of entropy of the system.

 

System  :  Closed

 

Process :  Constant volume since the gas is stirred in an rigid container

 


 3 .922  kJ/K    =

Comment : Though this process is adiabatic it is not isentropic since the process of stirring is an irreversible process.

 

Prob : 5.6 An insulated rigid vessel is divided into two chambers of equal volumes. One chamber contains air at 500 K and 2 MPa. The other chamber is evacuated. If the two chambers are connected d, what would be the entropy change ?

 

System  :  Closed system

 

Process :  Unresisted expansion

 


=0.199 kJ/kgK

 

Comment  :   Though the process is adiabatic entropy increases as the process involving

 

unresisted expansion is an irreversible process. It also proves the fact



Prob : 5.7 An adiabatic chamber is partitioned into two equal compartments. On one side there is oxygen at 860 kPa and 14oC. On the other side also, there is oxygen, but at 100 kPa and 14oC. The chamber is insulated and has a volume of 7500 cc. The partition is abruptly removed. Determine the final pressure and the change in entropy of the universe.




Prob : 5.8 A closed system is taken through a cycle consisting of four reversible processes. Details of the processes are listed below. Determine the power developed if the system is executing 100 cycles per minutes.

 






 


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