Thermodynamics for Engineering Students

Review work, kinetic energy, and potential energy and derive how the change in kinetic energy equals work done by forces. Explore gravity's role in potential energy and energy conservation.

Apply kinetic and potential energy equations to a 100 pound weight, deriving mass from weight and gravity, to find velocity and height: v2 about 35.7 ft/s and h2 45 ft.

Explore thermodynamic work as energy transfer with sign conventions for positive work by the system and negative work on the system, using W = ∫ P dV.

an example analyzes a piston-cylinder process for CO2, calculating the work by integrating the pressure–volume curve and converting units to British thermal units, with work done on the system.

Draw the PV diagram for a piston cylinder gas undergoing three sequential processes—constant volume, PV-constant compression, and constant-pressure expansion—and compute the work in kilojoules, noting zero work for constant volume.

Apply the PV^n relation in a piston-cylinder gas expansion to determine initial pressure and the work, noting sign conventions for work on or by the system.

Assess a three-step piston cylinder cycle for carbon monoxide gas, tracing constant-pressure expansion, constant-volume cooling, and compression, and compute the work in kilojoules from a PV diagram.

Explore how internal, kinetic, and potential energies form total energy changes, and apply heat transfer concepts with Q, Q dot, and adiabatic (no heat transfer) processes.

Apply the first law for a closed system, using energy balance delta E equals heat minus work, to track changes in kinetic, potential, and internal energy.

Apply the closed-system energy balance delta U plus delta PE plus delta K equals q minus W to determine heat transfer. Convert per-mass terms to totals and interpret q's sign.

Analyze a piston-cylinder transition from state 1 to state 2 through two processes, A and B, noting constant PV and constant-volume/linear PV paths with work and heat.

analyze a gas in a piston-cylinder with PV^1.2 behavior, applying energy balance to determine the change in specific internal energy from the given heat transfer and computed work.

Understand how thermodynamic cycles return to the initial state, making Q in equals W. Explore power, refrigeration, and heat-pump cycles with Q in, Q out, and COP.

Analyze a three-process piston-cylinder thermodynamic cycle with pv = constant compression, constant-volume, and constant-pressure legs; compute the cycle work, heat transfer for 2-3, and identify refrigeration.

Examine a piston-cylinder gas cycle with constant-pressure, PV constant compression, and constant-volume processes to compute the cycle work and heat transfer.

analyze a gas cycle in a piston-cylinder with three processes, compute state energies and heat transfers, and determine if the cycle delivers power using the energy balance.

Explore how to evaluate properties by defining homogeneity, phases, pure substances, and simple compressible systems, and examine the PBT surface and vapor dome, including saturation and critical points.

Heat water in a piston cylinder at fixed pressure to trace the vapor dome from compressed liquid to saturated liquid, two-phase mixture, saturated and superheated vapor, illustrating latent heat.

Learn to navigate steam tables for water, identify when to use compressed liquid or superheated vapor, convert between SI and English units, and apply linear interpolation for missing data.

Master the vapor dome, saturated liquid and vapor, and the quality concept as you study steam tables a2 and a3 for specific volume and internal energy in liquid-vapor mixtures.

Learn to use steam tables and the tv diagram to determine pressure, specific volume, and state for water across compressed liquid, saturated, and superheated conditions.

Learn to use a steam table flow chart to identify compressed liquid, saturated vapor, or superheated vapor from pressure and temperature, and select the appropriate table for properties.

Apply steam-table methods to a closed, rigid tank with a two-phase refrigerant, tracking quality and vapor mass as it heats from 10 degrees celsius to 50 degrees celsius using tv diagrams and vf/vg interpolation.

Locate three states on the PV and TV diagrams using steam tables, showing compressed liquid, liquid–vapor mixture, and superheated vapor along an isothermal line.

Trace a piston-cylinder water process at 20 psia, from 50 °F liquid through saturated liquid, saturated vapor, to 300 °F superheated vapor, and compute work and heat transfer per pound.

Determine the tank volume for a 10 bar two‑phase refrigerant with 25 kg saturated liquid and 60% quality using v_f and v_g; total volume ≈ 0.906 m^3, vapor ≈ 97.7%.

an example analyzes a rigid, insulated tank with 0.14 lb water in a two‑phase state at 20 psia, computing volume, initial temperature, and final pressure as it becomes saturated vapor.

Explore approximating liquid properties with saturated liquid data from the liquid-vapor table, estimating Vf and Uf at a given temperature, and applying incompressible-substance assumptions to entropy and enthalpy.

Explore the generalized compressibility chart and the compressibility factor Z, relate it to the ideal gas law, and use reduced pressure and temperature to determine Z for gases.

Derive ideal gas relations from the ideal gas law, linking internal energy and enthalpy to temperature via CV and CP, and introduce gamma and entropy concepts.

Calculate water volume at 100 bar and 400 degrees Celsius using compressibility charts and steam tables, compare results, and assess ideal gas assumptions and z-factor accuracy.

Compute the work for a closed butane piston-cylinder under isothermal compression by using compressibility data, reduced properties, and a logarithmic expression to obtain w/m in kilojoules per kilogram.

Review polytropic relations and ideal gas behavior using P1V1^n = P2V2^n and PV = RT to reveal isothermal conditions when n = 1.

demonstrates an ideal gas expansion of carbon dioxide in a piston cylinder, using P V^(1.2) and the energy balance to determine final pressure, work, and heat transfer.

An ideal gas piston-cylinder expands polytropically from 600 R and 20 ft^3 to P2 51.4 psia, V2 34.8 ft^3, T2 537 R, with Q ≈ 97 Btu and W positive.

Calculate the heat transfer for a constant-pressure expansion of 2 kg oxygen from v1=2 m^3 to v2=4 m^3 at p1=1 bar, using ideal gas relations with gamma=1.35 and constant cv.

Apply conservation of mass in a control volume to derive the mass flow balance for inlets and outlets. Analyze one-dimensional flow with uniform velocity and density, and steady-state simplifications.

Calculate the air mass flow rate through a turbine using the ideal gas relation with 200 kPa, 150 degrees Celsius, and 7000 liters per second, converting to kilograms per second.

Apply a mass-balance calculation to a mixing tank with two inlets and one outlet to determine the water mass after 30 minutes, using inflows minus outflow.

an iso-thermal steady flow problem analyzes liquid water in a duct with diameters 0.02 m and 0.04 m to determine exit velocity and mass flow rate using specific volume.

Apply ideal gas and steady-state flow to compute mass flow rate and exit area for air using m_dot = rho A v and p = rho R T.

Apply conservation of energy to a control volume by accounting for heat transfer, work, and the energy carried by mass flow (enthalpy, kinetic, and potential terms) at inlets and outlets.

Use the ideal gas model on air in a well insulated pipe to find v1, v2, and mass flow from 600 kPa 330 K to 120 kPa 300 K.

Apply an energy balance to the outside and return air in a chiller ducting system to determine the exit temperature and diameter, assuming ideal gas behavior and no heat transfer.

apply steady-state energy balance to a steam turbine: inlet 700 °f, 450 psi; exit saturated vapor at 1.2 psi; compute inlet volumetric flow rate from mass flow and specific volume.

Explore how nozzles speed up flow by reducing cross-sectional area and how diffusers slow it, raising exit pressure. Apply steady-state mass-flow equations and consider flow work and kinetic energy changes.

Apply the steady-state energy balance to an air nozzle using the ideal gas model to compute inlet area and heat transfer with given mass flow, speeds, and temperatures.

Apply the steady-state control-volume energy balance to a turbine with 20 percent extraction, determining inlet mass flow from power, heat transfer, and saturated vapor conditions.

Analyze a multi-stage steam cycle with a reheater to determine mass flow rate, total turbine power, and reheater heat transfer using steady-state energy balance and enthalpy lookups.

Determine the inlet area for a steady-state turbine with 15 kg/s steam (v1=100 m/s at 2 MPa, 360°C) and compute heat transfer to surroundings (≈ −313 kW).

Apply the energy balance to compressors and pumps at steady state with insulation to determine volumetric flow rates and the required power input using saturated and superheated refrigerant tables.

This lecture covers heat exchangers with a condenser example where refrigerant transfers heat to cooling water under steady-state conditions, computing 33.16 gpm and 3.30e5 Btu/hr.

Analyze a heat exchanger in an air conditioning system where air and refrigerant 134a exchange heat; apply steady-state energy balance to compute refrigerant mass flow rate and heat transfer.

Explore throttling devices that lower pressure by restriction, using h1 = h2 across the valve. In the ammonia expansion example, 10 bar to 1 bar yields a quality around 0.20.

An example analyzes air and water flows through two compressors and a heat exchanger, using steady-state energy balances and ideal gas assumptions to determine compressor powers and water flow rate.

Explore the second law of thermodynamics, including the classiest and Kelvin-Planck statements, with single-reservoir constraints and the role of irreversibility in cycle feasibility.

Analyze a reversible power cycle by calculating thermal efficiency and heat transfers Q_H and Q_C for hot and cold reservoirs using T_H and T_C, with Kelvin and unit conversions.

Analyze a power cycle exchanging heat between hot (1200 rankine) and cold (400 rankine) reservoirs to classify each case as irreversible, reversible, or impossible using efficiency versus max efficiency.

Explore the Kelvin absolute temperature scale and the max performance equations for power, refrigeration, and heat pump cycles, including Kano efficiency and reversible cycle relationships.

Analyze four data sets for a power cycle between hot 1500 kelvin and cold 450 kelvin, using Q_H, Q_C, and work to classify reversible, irreversible, or impossible cases. Compare the cycle's efficiency to the max efficiency 1 minus Tc/Th to identify physically allowable scenarios.

Determine the thermal efficiency of a power cycle and the energy discharged to the cold reservoir for a 1000 BTU heat input, using 0.36 actual and 0.48 reversible efficiencies.

Explore the Carnot cycle, a theoretical four-step, internally reversible engine with two no heat transfer and two isothermal processes, drawn on a Peavey diagram and its maximum thermal efficiency.

An in-depth Kano cycle example analyzes iso-thermal expansion from saturated liquid to saturated vapor, 80% expansion to 100 f with x=0.703, using a pv diagram to compute heat and work.

Compute the cycle heat and work from each process, confirm energy balance, and determine efficiency using Qh and the Carnot limit, showing a near 41.7% for a reversible cycle.

Analyze a steady-state refrigeration system with a COP of 5 and a 23 °C kitchen. Determine the power input as 2.8 kW and the lowest Tc as 246.7 K.

Explore the Clausius inequality and how to assess irreversibility in a power cycle using sigma cycle, Qh, Th, QC, Tc, and thermal efficiency scenarios.

Explore entropy as a state function and disorder, link internally reversible cycles with the Clausius inequality, and define entropy and specific entropy, including the TdS relation and phase-change forms.

Develop entropy change for an incompressible system and for ideal gases, deriving D S = C_v dT/T and D S = C_p dT/T with V and P terms.

analyze a 1 kg water iso-thermal compression to saturated liquid in a piston cylinder, compute heat transfer and entropy change using specific internal energy and entropy from tables.

Compute entropy change for nitrogen, 5 kg of ideal gas, from 5 bar 400 K to 2 bar 500 K using constant and variable cp from tables A20 and A23.

Analyze entropy change in closed systems via internally reversible processes, showing how heat transfer alters entropy with dS = dq/T, and explain isentropic (constant entropy) conditions on a T-S diagram.

Explore an internally reversible water-piston cylinder process from 10 psi 500 f to 80 psi 800 f to determine heat and work per pound using entropy and the temperature-entropy relation.

Derive the entropy balance for closed systems, relate entropy change to heat transfer and internal production, and apply the differential rate form to identify irreversibility.

Compute Q in Btu and entropy produced in Btu per Rankine for 10 lb air in a rigid tank heated 600 R to 800 R by 900 R reservoir.

Analyze a rigid, insulated water system with a paddle wheel from 60 °F at 60% quality to 350 °F, calculating work from Δu and entropy produced from Δs.

Apply control-volume entropy balance with mass flow to a steady-state turbine and heat exchanger, accounting for inlet and outlet entropy and entropy production, then rank components by efficiency.

Analyze an open feed water heater, a direct-contact heat exchanger in vapor power plants, at steady state to compute the entropy production rate via the entropy balance.

Explore the isentropic (constant-entropy) process for an ideal gas, deriving P2 from P1 using the natural log and exponential relations, and using PR values from table A22.

Analyze argon in a piston-cylinder undergoing ice and tropic processes with P1=150 kPa, P2=300 kPa, T1=35 C, and k=1.67, using the ideal gas model to find T2 and work per kilogram.

Isentropic compression of air in a cylinder (ideal gas) from 30 psi, 6 ft^3 to 1.2 ft^3 yields mass ~0.95 lb, P2 ~285 psi, T2 ~2971 R, W ~ -74 pounds.