A system absorbs 500 J of heat and does 300 J of work. The change in internal energy is:
A
200 J
B
800 J
C
-200 J
D
500 J
First law: ΔU = Q - W = 500 - 300 = 200 J (using convention W = work by system).
What does the Gibbs free energy criterion ΔG < 0 indicate for a process?
A
Process is non-spontaneous at all temperatures
B
Process is spontaneous and irreversible
C
Process is at equilibrium
D
Process releases maximum useful work
Correct Answer:
B. Process is spontaneous and irreversible
ΔG < 0 indicates spontaneous, irreversible process under constant T and P conditions.
For a system at equilibrium, the chemical potential of a substance in different phases must be:
A
Equal
B
Different
C
Zero
D
Proportional to temperature
At phase equilibrium, μ_liquid = μ_vapor = μ_solid. This equality determines equilibrium conditions.
What is the Clausius-Clapeyron equation used for?
A
Calculating work done in cyclic processes
B
Relating vapor pressure to temperature during phase transitions
C
Determining heat capacity of substances
D
Calculating entropy of mixing
Correct Answer:
B. Relating vapor pressure to temperature during phase transitions
Clausius-Clapeyron equation: ln(P₂/P₁) = -(ΔH_vap/R)(1/T₂ - 1/T₁) describes phase equilibrium.
In the van der Waals equation, the term 'a' represents:
A
Volume correction due to molecular size
B
Pressure correction due to intermolecular attractive forces
C
Temperature correction factor
D
Compressibility factor at critical point
Correct Answer:
B. Pressure correction due to intermolecular attractive forces
In (P + a/V²)(V - b) = RT, 'a' corrects for intermolecular forces reducing pressure, while 'b' corrects for molecular volume.
A gas undergoes an isothermal expansion from 2 L to 5 L at 298 K. If the process is reversible, what is the sign of entropy change for an ideal gas?
A
Positive
B
Negative
C
Zero
D
Cannot be determined
Correct Answer:
A. Positive
For isothermal expansion of an ideal gas, ΔS = nR ln(V_f/V_i) = nR ln(5/2) > 0. Volume increases, so entropy increases.
During a constant volume process, the first law of thermodynamics simplifies to:
A
ΔU = q + w = q - PΔV
B
ΔU = q (since w = 0 at constant volume)
C
ΔU = w (since q = 0 in all processes)
D
ΔU = 0 (no energy change)
Correct Answer:
B. ΔU = q (since w = 0 at constant volume)
At constant volume, ΔV = 0, so w = -P∫dV = 0. Therefore, ΔU = q + w = q + 0 = q. All heat goes into internal energy change.
For a binary ideal solution, the total vapor pressure at constant T is given by:
A
P = P₁°x₁ + P₂°x₂ (Raoult's law)
B
P = P₁°/x₁ + P₂°/x₂
C
P = (P₁° + P₂°)/(x₁ + x₂)
D
P = P₁° + P₂° regardless of composition
Correct Answer:
A. P = P₁°x₁ + P₂°x₂ (Raoult's law)
Raoult's law states P_i = P_i°x_i for ideal solutions. Total pressure P = P₁°x₁ + P₂°x₂. This assumes ideal mixing behavior.
In a constant pressure process, the heat absorbed by a system equals:
A
Change in internal energy only
B
Enthalpy change
C
Work done by the system
D
Change in entropy
Correct Answer:
B. Enthalpy change
At constant pressure, q_p = ΔH (change in enthalpy). This is the definition of enthalpy and is a key relationship in engineering thermodynamics.
For an ideal gas undergoing adiabatic compression, the entropy change is:
A
Positive
B
Negative
C
Zero
D
Indeterminate without volume ratio
For a reversible adiabatic process, dq = 0, therefore ΔS = ∫dq_rev/T = 0. Entropy remains constant during reversible adiabatic processes.
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