Fundamentals of Engineering Thermodynamics

Explore energy concepts under the first law of thermodynamics, including kinetic and potential energy, work and heat transfer, and energy balances, with applications to power, refrigeration, and heat pump cycles.

Explore work and power in thermodynamics: work equals the integral of P dV, sign conventions distinguish expansion versus compression, and PV diagrams reveal polytropic P V^n relations.

Air in a piston-cylinder is slowly compressed from state 1 to 2 linearly, then at constant pressure to state 3; compute total work from the P–V curve areas.

Analyze a gas in a piston through a three-process thermodynamic cycle—an isothermal expansion, constant-volume heating, and constant-pressure compression—calculate the total work and sketch the PV diagram.

Understand internal energy as energy stored in springs, batteries, and heated fluids, from microscopic motion and chemical bonds. Identify how state changes split energy into kinetic, potential, and internal forms.

Learn how energy transfers by heat are quantified with q and q̇, and how conduction, convection, and radiation govern heat flow using k, h, ε, and sigma.

Compute convection and radiation heat transfer per unit area from a 47 °C grill surface to a 20 °C environment using h = 10 and ε = 0.93; sum rates.

Apply first law to a closed system, linking energy change to heat transfer and work with ΔE = Q − W and dE/dt = Q̇ − Ẇ under steady state.

Example 5 applies the first law to a gas expansion using P V^n with n=1.5, computing the work and change in internal energy to determine the heat transfer.

Apply the first law to a piston at constant pressure, relate heat transfer, work, and internal energy change, and compute q12 from ΔU and W.

At steady state, the gearbox energy balance uses the first-law rate form, accounting for 1.2 kW convection heat loss and yielding 58.8 kW output from a 60 kW input.

Apply the first law to cycles; energy change is zero. Rely on two reservoirs; refrigeration uses cooling load over work, while heat pumps use heat output over work.

Analyze transistor cooling by convection: compute heat transfer rate at steady state using the first law and find surface temperature with air at 25 C, h=100, area 5e-4 m^2.

Pure substances have uniform composition across phases; water illustrates phase changes from compressed liquid to saturated liquid, saturated vapor, and superheated vapor at 1 atm with latent heat.

Explore how tv and pv diagrams map water’s phase changes, from 1 atm heating to saturation and liquid–vapor equilibrium, to the critical point, compressed and saturated regions, and superheated vapor.

Define enthalpy h, equal to u + p v, and apply it to constant-pressure heating. The first law shows heat input equals delta h, clarifying heating vs constant-volume processes.

Learn to analyze saturated liquid–vapor mixtures on the TV diagram using quality x to compute average properties like specific volume and internal energy from Vf, Vg, Uf, Ug.

Identify the superheated vapor region on the TV diagram and use the tables to read properties such as specific volume and internal energy at a given pressure and temperature.

Learn to identify compressed liquid states on the TV diagram, with pressure above P_sat and temperature below T_sat, and use saturated liquid data for properties when pressure effects are small.

Learn linear interpolation to estimate properties between table values, using water in the superheated region to determine specific volume from tables A3 and A4.

Analyze constant-volume heating of a 0.5 m^3 rigid tank from a 50/50 liquid–vapor state at 1 bar, locating states on a TV diagram and finding P3 by interpolation.

Trace a three-state water process: superheated vapor at 400°C, saturated vapor at 10 bar, constant-volume cooling to a liquid-vapor mixture; apply first law to compute work and heat per kg.

Define cv and cp and explain their difference during constant volume and constant pressure heating. Illustrate with helium and the incompressible substance model for solids and liquids.

Study the generalized compressibility chart and the Z factor for real gases. Learn when reduced pressure and temperature justify ideal gas behavior and where deviations occur near the critical point.

Learn to evaluate ideal gas properties by linking internal energy and enthalpy to temperature, using cp, cv, and gamma, with tables for air and other gases.

Explore polytropic process relations for ideal gases, derive temperature-pressure and temperature-volume relationships, and compute work and internal energy changes during polytropic processes.

Analyze two connected tanks of carbon monoxide and air, mix with heat transfer, apply ideal gas law to find final pressure and use the first law to compute heat transfer.

Apply first law to a two-phase water mixture in a piston cylinder, performing constant-pressure heating (1→2) and constant-volume heating (2→3) to determine heat and work from state 1 to 3.

Explore a two-step cooling of water in a piston-cylinder: constant-pressure expansion to half volume, then constant-volume cooling to 25 degrees Celsius, calculating states, work, and heat transfer.

Apply the first law to an ideal helium gas in a piston: derive Cv from Cp and R, determine T2 at 500 kPa, and compute constant-volume heat transfer.

Solve a well-insulated, rigid container problem with two ideal gases, air and carbon monoxide, separated by a movable partition; determine the equilibrium temperature and pressure after conduction between gases.

Analyze a four-process power cycle for an ideal gas with constant specific heat, calculating work and heat per process and evaluating cycle efficiency in engineering thermodynamics.

Derives conservation of mass for a control volume by equating inflow and outflow to the rate of change of mass, defining the mass flow rate with area, density, and velocity.

Apply a mass balance to a two-inlet water heater to compute section 2 mass flow from section 3 exit using saturated-liquid data at 7 bar and 40 °C for v2.

nozzles accelerate flow by decreasing area, while diffusers decelerate flow to raise pressure; the first law yields h1-h2 = (v2^2 - v1^2)/2 for adiabatic, same height.

Calculate the exit area of a steam nozzle via energy balance with zero heat transfer and no work, deriving specific volume from P and T to support mass flow calculations.

Solves a compressor power problem at steady state, accounting for heat loss and kinetic-energy changes, using the first law and ideal gas air properties to compute power input in kilowatts.

Apply the first law to a steam turbine to compute heat transfer with inlet superheated steam at 60 bar, 400 degrees Celsius, and outlet at 0.1 bar with quality.

Explore concentric tube heat exchangers where hot fluid A transfers heat to cold fluid B without mixing, using first law balances for single or double-system configurations and mixing chamber concepts.

Evaluate a power plant condenser as a well-insulated heat exchanger at constant pressure, determining the cooling water to steam mass flow ratio and the heat transfer per kilogram of steam.

throttling devices cause a large pressure drop with no work done, keeping enthalpy constant (isenthalpic) and cooling the fluid, which is key in refrigeration and air conditioning.

Apply a throttling energy balance to find the saturation pressure of refrigerant R-134a at minus 8 C; analyze heat exchanger with water and compute water mass flow.

analyze a two-stage steam turbine with interstage heat exchanger reheating at constant pressure, from 140 bar and 500 c to 0.6 bar saturated vapor, calculating mass flow and total work.

Assess the thermal efficiency of a simple steam power plant cycle and compute the cooling water mass flow rate needed to condense the steam in the condenser.

Apply energy balance to a nitrogen compressor–heat exchanger with a helium cooling stream, using ideal gas assumptions to determine enthalpy changes and 0.25 kg/s mass flow under 50 kw input.

Explore reversible and irreversible processes under the first law of thermodynamics, and see how friction, mixing, and expansion influence energy transfer and thermodynamic cycle efficiency.

Explore reversible expansion and its maximum work compared with irreversible expansion. Splitting the driving mass into more steps increases expansion work toward the reversible limit.

Define a thermal reservoir and examine reversible heat transfer versus irreversible transfer. Demonstrate that finite reservoirs leave residual energy, and that smaller temperature differences and more reservoirs move toward reversibility.

Explains internally reversible processes with no boundary irreversibility, externally reversible processes with finite temperature differences, and totally reversible processes with infinitesimal temperature differences, and the forward and reverse paths coincide.

Explore heat engines, where high-grade heat converts to work with limits set by the second law. Understand Qh, Qc, cycle efficiency, and Kelvin-Planck and Clausius statements.

Carnot cycle comprises four reversible processes: isothermal expansion at TH, adiabatic expansion, isothermal compression at TC, and adiabatic compression, yielding maximum efficiency 1 - TC/TH.

Explore the reversed Carnot cycle, turning the Carnot power cycle into a refrigeration cycle by reversing processes, requiring input work to move heat from cold to hot.

Learn the Carnot principles: between the same hot and cold reservoirs, a reversible engine has constant efficiency, and irreversible engines exhibit lower efficiency than reversible ones.

Explain the Carnot efficiency as the maximum for heat engines between hot and cold reservoirs. Recognize that higher source temperatures yield more work and better energy quality.

Explore the Carnot refrigerator and heat pump operating between two thermal reservoirs, and learn how cop and gamma determine performance for reversible versus irreversible cycles.

Analyze a steady-state power cycle between a hot reservoir at 1800 kelvin and a cold reservoir at 600 kelvin, assessing reversibility, feasibility, and energy balance through efficiency calculations.

analyze a heat engine cycle between a 500 kelvin hot reservoir and a 300 kelvin cold reservoir, with a 0.1 mw output and a minimum heat rejection of 0.163 mw.

This example analyzes a steady-state refrigerator with cop 5 that absorbs interior heat and rejects 4.8 kw, giving about 0.8 kw input and a 246.7 k interior limit.

Analyze a cycle with Q1 750 kJ at 1500 K, Q2 100 kJ at 500 K, and Q3 at 1000 K; derive thermal efficiency versus sigma cycle and linear relation.

Analyze a power cycle with heat in at 525 K and out at 350 K, applying Clausius inequality, find sigma = 0 and a 33.3% efficiency, matching the Carnot limit.

Entropy is a property defined by path independence, shown via reversible cycles. Delta S equals the integral of dq over T from state 1 to 2, with units J/K.

Apply the same method used for pressure and temperature to retrieve entropy data, using the T-s diagram regions from compressed liquid to superheated vapor and applicable approximations.

Compute entropy change for 5 kg of refrigerant-134a in a rigid tank cooling from 140 kPa and 20°C to 100 kPa, using tables to determine S1, S2, and vapor quality.

Explore entropy change for an incompressible substance at constant volume, where internal energy depends on temperature, and assume constant cp. The entropy change is cp ln(T2/T1) for liquids and solids.

Derive the entropy change of an ideal gas by integrating S = C_V dT/T + R dV/V, giving ΔS = C_V ln(T2/T1) + R ln(V2/V1).

Explore the work and heat per unit mass for water from saturated liquid at 150 °C to saturated vapor at constant pressure, using entropy changes and a p–V analysis.

Apply the entropy rate balance for closed systems, with constant boundary temperature, by relating the time rate of entropy change to boundary entropy transfer and internal production due to irreversibility.

Determine entropy production rate in a gearbox at steady state with 60 kW input, 1.2 kW heat loss, and a 293 K boundary, highlighting friction as irreversibility and heat transfer.

Apply the entropy balance to an isolated system and its surroundings, showing that the total entropy increases for any irreversible process, guiding the direction of change.

Explore the entropy rate balance for a control volume, including entropy change, heat transfer, mass flow transfer, and entropy production, with steady-state implications and the nonconservation of entropy.

Apply the first law and entropy balance to a turbine with steam entering at 32 bar and 400 C, exiting as vapor at 100 C, yielding entropy production ≈0.498 kJ/kg-K.

Explore isentropic processes in thermodynamics, derive zero entropy change for reversible closed systems and control-volume processes, and relate temperature, pressure, and quality along isentropic paths.

an ideal steam process from 6 mpa and 400 c to a lower pressure is adiabatic and reversible, preserving entropy; compute work per mass from h1 and h2 with state 2 as a near vapor mixture (x ≈ 0.99).

Compute isentropic compression of air with a compression ratio of 8, starting from 22 °C and 95 kPa, yielding T2 ≈ 677.7 K and P2 ≈ 1,746 kPa.

Explore isentropic turbine efficiency by comparing actual versus ideal isentropic expansions, using entropy balance and the first law to relate state 1 and 2, enthalpy changes, and work output.

Compute the isentropic efficiency of an ideal-gas turbine expanding from 3 bar and 390 K to a lower pressure, using Cp and gamma, with 74 kJ/kg actual work.

Compare actual specific Carnatic energy at the nozzle exit to the ideal isentropic expansion under identical inlet and exit pressure conditions, with nozzle efficiencies typically between 90 and 95 percent.

Determine the maximum nozzle exit velocity using the 0.92 isentropic efficiency and the first law between states 1 and 2, with state 1 at 950 K.

Define isentropic compressor and pump efficiencies as the isentropic work over the actual work. Actual compression requires more work than isentropic compression, so efficiency remains below one.

Analyze a compressor raising pressure from 100 kPa to 1800 kPa at 0.2 kg/s with 80% isentropic efficiency; determine the actual exit temperature and required power.

Derive reversible work for a steady-flow device using the first law and control volume analysis, showing w dot reversible equals minus integral p dV; compare liquids and gases.

Compare the work to compress a saturated liquid with a pump versus a saturated vapor with a compressor from 100 kPa to 1 MPa.

Minimize compressor work by cooling between stages and using two-stage compression with intercooling; compare polytropic, isentropic, and isothermal paths on PV diagrams.

Compare the compressor work per unit mass for an irreversible compression from 100 kPa and 300 K to 900 kPa, across isentropic, polytropic with n=1.3, isothermal, and two-stage intercooling cases.