An ideal gas at 300 K and 200 kPa is compressed isothermally to 400 kPa in a piston-cylinder device. If the initial volume is 0.5 m³, what is the final volume?
Thermodynamics
Question · Medium
A Carnot heat engine operates between a source at 800 K and a sink at 300 K. What is the maximum theoretical thermal efficiency?
According to the first law of thermodynamics for a closed system undergoing a process, which expression is correct?
Question · Easy
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Steam at 2 MPa with a quality x = 0.85 enters a turbine. Which property set must be consulted from steam tables to determine the specific enthalpy?
Air in a rigid insulated tank (ΔQ = 0, ΔV = 0) is stirred by a paddle wheel adding 50 kJ of shaft work. If the internal energy increases by 50 kJ, the process is:
Question · Hard
The second law of thermodynamics states that the entropy of an isolated system:
An ideal gas with k = 1.4 expands isentropically from P₁ = 500 kPa to P₂ = 100 kPa. What is the temperature ratio T₂/T₁?
In a vapor-compression refrigeration cycle, the purpose of the throttling valve is to:
A heat pump delivers 3 kW of heat to a building while consuming 1 kW of electrical power. What is the coefficient of performance (COP)?
Which thermodynamic property is NOT a state function?
A gas turbine Brayton cycle with pressure ratio r = 8 and k = 1.4 has approximate ideal thermal efficiency η = 1 − r^((1−k)/k). What is η?
During a constant-pressure process, 200 kJ of heat is added to air in a piston-cylinder device. If the boundary work is 80 kJ, the change in internal energy is:
The Maxwell relation (∂T/∂V)_S = −(∂P/∂S)_V is derived from:
Wet-bulb temperature is primarily used in psychrometrics to determine:
A refrigerator maintains a cold space at −10°C while rejecting heat to 30°C ambient. What is the maximum possible COP_ref?
Water (ρ = 1000 kg/m³) flows through a horizontal pipe that narrows from diameter 10 cm to 5 cm. If velocity in the large section is 2 m/s, what is velocity in the small section?
Fluid Mechanics
The Reynolds number for water at 20°C (ν = 1×10⁻⁶ m²/s) flowing at 2 m/s in a 50 mm diameter pipe is approximately:
According to Bernoulli's equation for steady incompressible inviscid flow along a streamline, which quantity remains constant?
A U-tube manometer with mercury (ρ_m = 13,600 kg/m³) shows a height difference of 200 mm between the two limbs. The gauge pressure of the connected gas (ρ_gas negligible) is approximately:
The Moody diagram relates friction factor f to:
A centrifugal pump adds 30 m of head to water. If flow rate is 0.05 m³/s and pump efficiency is 80%, the required shaft power is approximately:
In fluid statics, the hydrostatic pressure increase with depth in a liquid of density ρ is given by:
The venturi meter measures flow rate by exploiting:
For laminar fully developed flow in a circular pipe, the ratio of maximum velocity to average velocity is:
Buckingham Pi theorem is used in fluid mechanics to:
A flat plate 2 m wide moves at 5 m/s through still oil (μ = 0.5 Pa·s). Estimate order of magnitude for Reynolds number based on plate length 1 m (Re_L = ρUL/μ, ρ = 900 kg/m³):
Cavitation in pumps occurs when local pressure drops below:
The Darcy-Weisbach equation for head loss in pipe flow is:
An ideal fluid is defined as one with:
Torricelli's theorem gives exit velocity from a tank as V = √(2gh). This assumes:
A plane wall 0.2 m thick has thermal conductivity k = 50 W/(m·K). Steady heat flux through the wall is 2500 W/m². The temperature drop across the wall is:
Heat Transfer
Newton's law of cooling for convection is expressed as:
A blackbody at 500 K radiates energy. If temperature increases to 1000 K, the radiative heat flux increases by a factor of:
The Biot number Bi = hL/k is used to determine whether:
In a counterflow heat exchanger, the log mean temperature difference (LMTD) is generally:
A straight fin of length L with tip convection has efficiency that increases when:
Thermal resistance for conduction through a cylindrical wall (r₁ to r₂) is:
Nusselt number Nu = hL/k represents the ratio of:
A 5 mm thick glass window (k = 1.0 W/(m·K)) has inside air h_i = 10 W/(m²·K) and outside h_o = 25 W/(m²·K). Overall U-value (center of glass) is approximately:
Critical insulation radius for a cylinder occurs when adding insulation:
Phase change heat transfer during boiling at saturation temperature is characterized by:
Prandtl number Pr = μcp/k is important because it relates:
A steel plate at 400°C is quenched in water at 25°C. The dominant initial heat transfer mechanism at the surface is:
Steady one-dimensional conduction with internal heat generation ġ (W/m³) in a plane wall with both sides at T₀ has maximum temperature at:
A solid circular shaft 40 mm diameter transmits 50 kW at 300 rpm. The torque transmitted is approximately:
Machine Design
For a ductile material under combined normal and shear stress, the von Mises (distortion energy) criterion compares:
A spur gear with 20 teeth and module m = 3 mm has pitch circle diameter of:
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