Test: Entropy - 3 - Mechanical Engineering MCQ

If  Cycle is reversible
If Cycle is irreversible
If Cycle is impossible
Hence
For cycle is possible 
This is known as Clausius inequality.

δQ = dU+ PdV... Applicable for a closed system when only PdV work is present. This is true only for a reversible process.
δQ = TdS ...Applicable for a reversible process.
TdS = dU + PdV... Applicable for any process reversible or irreversible, undergone by a closed system, since it is a relation among properties which are independent of the path.

Subsystem 1 having a fluid of mass m₁ specific heat c₁ and temperature t₁ and subsystem 2 consisting of a fluid of mass m₂, specific heat c₂, and temperature t₂, comprise a composite system in an adiabatic enclosure figure. When the partition is removed, the two fluids mix together, and at equilibrium let t_f be the final temperature, and t₂ < t_f < t₁ Since energy interaction is exclusively confined to the two fluids, the system being isolated

∴  

Entropy change for the fluid in subsystem1,

This will be negative, since T₁ > T_f
Entropy change for the fluid in subsystem 2

This will be positive, since T₂ < T_f

ΔS_univ will be positive definite, and the mixing process is irreversible.
Although the mixing process is irreversible, to evaluate the entropy change for the subsystem, the irreversible path was replaced by a reversible path on which the integration was performed.

For isentropic expansion, PV^γ = constant

from ideal gas law,


Also, 

Every process proceeds in such direction that total entropy change associated with it will be positive.

For reversible adiabatic process, ΔS = 0 but ΔH ≠ 0.

We know that:
For closed cycle change in internal energy is zero First law of thermodynamic for closed system

Hence, equal area are enclosed by figures 1 and 2.

Explanation:

• Process 1-2: This process is represented by line AB in the T-S diagram. It is an isentropic compression process where the gas is compressed adiabatically and reversibly.


• Process 2-3: This process is represented by line BC in the T-S diagram. It is an isobaric heat addition process where the gas absorbs heat at constant pressure and the temperature and entropy increase.


• Process 3-4: This process is represented by line CD in the T-S diagram. It is an isentropic expansion process where the gas expands adiabatically and reversibly, doing work on the surroundings.


• Process 4-1: This process is represented by line DA in the T-S diagram. It is an isochoric heat rejection process where the gas releases heat at constant volume and the temperature and entropy decrease.