Entropy and Clausius Inequality
1 / 10
The Clausius inequality is expressed as:
∮ δQ/T ≥ 0
∮ δQ/T ≤ 0
∮ δQ/T = 0
∮ δQ = 0
 The Clausius inequality states that for any cyclic process, the integral of δQ/T (heat transfer divided by absolute temperature) is less than or equal to zero. For reversible cycles, it equals zero; for irreversible cycles, it is less than zero.
2 / 10
An irreversible process occurs in a system, and 200 kJ of heat is rejected to a reservoir at 300 K. The minimum entropy change of the universe is:
0 kJ/K
0.667 kJ/K
-0.667 kJ/K
1.0 kJ/K
 For an irreversible process, the entropy change of the universe is positive. The entropy change of the reservoir is ΔS_res = Q/T = 200/300 = 0.667 kJ/K. Since the system’s entropy change is unknown but the universe’s entropy must increase, ΔS_universe ≥ 0.667 kJ/K (minimum when the system’s entropy change is zero).
3 / 10
A gas expands isothermally and reversibly from state 1 to state 2. The entropy change of the system is given by:
ΔS = nR ln(V1/V2)
ΔS = nR ln(V2/V1)
ΔS = nR ln(T2/T1)
ΔS = 0
For a reversible isothermal expansion of an ideal gas, ΔS = nR ln(V2/V1), where V2 > V1, and n is the number of moles, R is the gas constant.
4 / 10
For a reversible process, the entropy change of the universe is:
Positive
Negative
Zero
Depends on the process
For a reversible process, the entropy change of the universe (system + surroundings) is always zero, as the entropy gained by one is exactly balanced by the entropy lost by the other
5 / 10
The entropy of a system can decrease if:
The process is irreversible
Heat is added to the system
The surroundings experience a greater entropy increase
The process is adiabatic
The entropy of a system can decrease (ΔS_system < 0) as long as the total entropy of the universe increases (ΔS_universe > 0), which requires the surroundings to have a larger entropy increase
6 / 10
A heat engine operates between two reservoirs at 600 K and 300 K. It absorbs 1000 kJ of heat from the hot reservoir. The maximum possible entropy change of the universe is:
1.67 kJ/K
3.33 kJ/K
5.0 kJ/K
For a reversible heat engine (maximum efficiency), the entropy change of the universe is zero. ΔS_universe = ΔS_hot + ΔS_cold = -Qh/Th + Qc/Tc = 0 for a reversible cycle.
7 / 10
The Clausius inequality is a direct consequence of:
First law of thermodynamics
Second law of thermodynamics
Zeroth law of thermodynamics
Third law of thermodynamics
The Clausius inequality is a mathematical statement of the second law, which governs the direction of heat transfer and entropy changes in thermodynamic processes.
8 / 10
A system undergoes a process where 500 kJ of heat is transferred to it at a constant temperature of 400 K. If the process is reversible, the entropy change of the system is:
1.25 kJ/K
2.0 kJ/K
0.8 kJ/K
 For a reversible isothermal process, ΔS = Q/T = 500/400 = 1.25 kJ/K.
9 / 10
For an irreversible process in an isolated system, the entropy change is:
Always zero
Always negative
Always positive
Can be positive or negative
According to the second law of thermodynamics, the entropy of an isolated system (or universe) increases for irreversible processes (ΔS > 0).
10 / 10
The entropy change of a system undergoing a reversible adiabatic process is:
Undefined
 A reversible adiabatic process is isentropic, meaning the entropy change of the system is zero (ΔS = 0).
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