Which of the following represents a state function?
A Work done by the system B Heat absorbed by the system C Internal energy of the system D Path followed during a process
Internal energy (U), Enthalpy (H), Gibbs energy (G) are state functions. Work and heat are path functions
For a closed system at constant volume, the first law of thermodynamics simplifies to:
A ΔU = Q - W B ΔU = Q C ΔU = W D ΔH = Q
At constant volume, W = P×ΔV = 0. Therefore, ΔU = Q - 0 = Q
The standard Gibbs free energy change (ΔG°) for a reaction at equilibrium is:
A Zero B Positive C Negative D Depends on temperature only
At equilibrium, ΔG = 0, which means ΔG° = -RT ln(K), and when ΔG° = 0, K = 1 (equilibrium)
A reversible adiabatic process for an ideal gas follows PVᵞ = constant. If γ = 1.4 and initial pressure is 1 atm with volume 1 L, what is the final pressure when volume becomes 0.5 L?
A 2.64 atm B 1.4 atm C 2.0 atm D 0.5 atm
P₁V₁ᵞ = P₂V₂ᵞ → P₂ = P₁(V₁/V₂)ᵞ = 1×(0 1
The Helmholtz free energy (A = U - TS) is the maximum useful work available at:
A Constant temperature and volume B Constant temperature and pressure C Constant volume and entropy D Constant pressure and entropy
Helmholtz free energy is defined at constant T and V. ΔA_max = W_useful (non-PV work)
For a van der Waals gas, the critical compressibility factor (Z_c) is approximately:
A 0.27 B 1.0 C 0.5 D 0.375
For van der Waals gas: Z_c = P_c V_c/(nRT_c) = 8 3
A heat engine operates between 600 K and 300 K. What is the maximum theoretical efficiency (Carnot efficiency)?
A 50% B 100% C 33.3% D 66.7%
η_Carnot = 1 - (T_C/T_H) = 1 - (600 300
The equation of state for a real gas that considers molecular volume and intermolecular forces is:
A PV = nRT B (P + an²/V²)(V - nb) = nRT C PV = nRT + BP D P = ρRT/M
This is the van der Waals equation where 'a' accounts for intermolecular forces and 'b' for molecular volume
For an open system, the steady flow energy equation relates enthalpy rather than internal energy because:
A Enthalpy is independent of pressure B It accounts for flow work (PV) at inlet and exit C Enthalpy is always greater than internal energy D Entropy remains constant
H = U + PV. The PV term represents flow work needed to push fluid across system boundaries in steady flow
When 100 g of ice at 0°C melts to water at 0°C at 1 atm, the entropy change is approximately (ΔH_fus = 334 J/g):
A 122 J/K B 1.22 J/K C 0.122 J/K D 12.2 J/K
ΔS = ΔH/T = (100×334)/273.15 ≈ 122.3 J/K = 1.223 kJ/K ≈ 1.22 J/K (in kJ/K)
The fugacity coefficient (φ) for an ideal gas is:
A Always 1 B Always less than 1 C Always greater than 1 D Depends on temperature only
For ideal gases, f = P (fugacity equals pressure), so φ = f/P = 1. Real gases have φ ≠ 1
A system undergoes a process where Q = 100 J and W = 60 J. The change in internal energy is:
A 160 J B 40 J C -40 J D 100 J
ΔU = Q - W = 100 - 60 = 40 J (First Law of Thermodynamics)
For a spontaneous process occurring at constant temperature and pressure, which condition must be satisfied?
A ΔH > 0 and ΔS > 0 B ΔG = ΔH - TΔS < 0 C ΔU < 0 D ΔS_universe = 0
For spontaneity at constant T and P: ΔG = ΔH - TΔS must be negative (ΔG < 0)
A throttle valve is used in a refrigeration cycle. This is an example of a(n) _____ process.
A Isentropic B Isothermal C Adiabatic irreversible D Isochoric
Throttling is an adiabatic (Q=0) but irreversible process with no work done, causing entropy increase
The Maxwell relation derived from Gibbs free energy (G = H - TS) is:
A (∂S/∂P)_T = (∂V/∂T)_P B (∂V/∂T)_P = -(∂S/∂P)_T C (∂P/∂T)_V = (∂S/∂V)_T D (∂T/∂V)_S = (∂P/∂S)_V
From dG = -SdT + VdP, the Maxwell relation is: (∂V/∂T)_P = -(∂S/∂P)_T
A gas mixture at 298 K contains H₂ and N₂. If the mixture obeys Amagat's law and the partial volumes are equal, what is the mole fraction of H₂?
A 0.5 B 0.67 C 0.33 D 0.75
Amagat's law: V_total = V_H₂ + V_N₂. If partial volumes are equal, each is 50%, so x_H₂ = 0.5
For a non-ideal binary mixture, the activity coefficient (γᵢ) deviates from unity when:
A The mixture is dilute B Intermolecular interactions are significant C The system is at very low pressure D The components are structurally similar
Activity coefficients account for non-ideal behavior due to intermolecular forces and molecular size differences
The Clausius-Clapeyron equation relates vapor pressure to temperature. Which assumption is NOT required for its derivation?
A Equilibrium between liquid and vapor phases B Constant enthalpy of vaporization C Vapor behaves as an ideal gas D The system is open
Clausius-Clapeyron requires phase equilibrium, constant ΔH_vap, ideal gas approximation, but works for closed systems
A reversible adiabatic process is also known as:
A Isentropic process B Isothermal process C Isobaric process D Isochoric process
A reversible adiabatic process has constant entropy (dS = 0), which defines an isentropic process. This is a fundamental concept in thermodynamics.
The enthalpy change for a constant pressure process equals:
A Heat absorbed by the system B Work done on the system C Change in internal energy D Heat released to surroundings
At constant pressure, ΔH = qₚ (heat at constant pressure). This is the definition of enthalpy and its primary application.
