An ideal gas at 300 K and 150 kPa occupies 2 m³. If pressure is increased isothermally to 300 kPa, what is the final volume?
Thermodynamics
Question · Medium
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For a closed system, the first law of thermodynamics with heat in positive and work out positive is:
Question · Easy
A Carnot engine operates between 600 K (hot) and 300 K (cold). What is the maximum thermal efficiency?
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Steam at 1 MPa with quality x = 0.90. To find specific enthalpy h, you need from steam tables at 1 MPa:
During an isobaric heating of an ideal gas, 500 kJ of heat is added and 200 kJ of boundary work is done by the gas. The change in internal energy is:
The Gibbs free energy change ΔG for a reaction at constant T and P indicates:
Raoult's law for an ideal solution states that the vapor pressure of component i is:
A binary mixture at 80°C has component A with P_A° = 40 kPa and x_A = 0.50 (ideal solution). What is P_A in the vapor?
The standard heat of reaction ΔH°_rxn is calculated from heats of formation by:
For an ideal gas undergoing isentropic compression with k = 1.4 from T₁ = 300 K to pressure ratio P₂/P₁ = 4, T₂ ≈
Question · Hard
The second law of thermodynamics for an isolated system requires that total entropy:
In a vapor-compression refrigeration cycle, the throttling valve causes:
A heat pump delivers 5 kW of heat while consuming 1.25 kW of electrical power. The coefficient of performance (COP) is:
Fugacity in chemical thermodynamics is best described as:
Wet-bulb and dry-bulb temperatures in psychrometrics are used to determine:
For a steady-flow device (no shaft work, negligible KE/PE changes), the energy balance simplifies to:
The Clausius-Clapeyron equation relates vapor pressure to:
An adiabatic flash drum separates a feed at known T and P into vapor and liquid phases by:
Which property is a state function?
A gas mixture contains 2 kmol N₂ and 1 kmol O₂. The mole fraction of N₂ is:
Fick's first law of diffusion states that molar flux is proportional to:
Transport Phenomena
Steady one-dimensional conduction through a plane wall with thickness L, area A, thermal conductivity k, and ΔT across the wall. Heat rate Q is:
Water flows in a 0.05 m diameter pipe at average velocity 2 m/s. The volumetric flow rate is approximately:
The Reynolds number Re = ρVD/μ characterizes:
For water at 20°C in a 0.01 m pipe at v = 1.5 m/s, with ρ ≈ 1000 kg/m³ and μ ≈ 0.001 Pa·s, Re ≈
Bernoulli's equation along a streamline (inviscid, steady, incompressible) states:
In laminar flow through a circular pipe, the velocity profile is:
The Darcy friction factor f in ΔP = f(L/D)(ρV²/2) for pipe flow depends on:
For turbulent flow over a flat plate, the convective heat transfer coefficient h generally increases when:
Stefan-Boltzmann law for radiative heat flux from a gray surface is:
A countercurrent heat exchanger: hot fluid 150°C → 90°C, cold fluid 30°C → 70°C. The LMTD is approximately:
The Nusselt number Nu is defined as:
Mass transfer coefficient k_G relates flux to:
For diffusion through a stagnant film of thickness δ with diffusivity D_AB, the mass transfer coefficient k_c ≈
The Prandtl number Pr = Cpμ/k indicates:
In a packed column for gas absorption, increasing liquid flow rate typically:
Boundary layer thickness in laminar flow over a flat plate generally:
Ergun equation is used to calculate:
An fin with effectiveness η_f < 1 means:
For a first-order reaction A → products with rate r_A = kC_A, the half-life t_{1/2} is:
Reaction Engineering
The design equation for an ideal CSTR is:
For a PFR, the volume required for conversion X_A is:
Arrhenius equation k = A exp(−E_a/RT) shows that reaction rate constant:
If E_a = 50 kJ/mol and R = 8.314 J/mol·K, at what temperature does the Arrhenius exponent E_a/RT equal approximately 10?
Selectivity in multiple reactions A → D (desired) and A → U (undesired) is commonly defined as:
A batch reactor holds 2 m³ of liquid. If volumetric flow is irrelevant and initial concentration C_A0 = 2 mol/L, moles of A initially present are:
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