- Derive the exergy balance for the exhaust stroke valid for the internal combustion engine model of Section 4.9, and comment on the outcome.
- Use TPSI with a program of your choice and generate the T–s diagram of n-butane. The diagram should contain the saturation lines enclosing the vapor liquid equilibrium region, the critical point
- The Lenoir cycle is a model for the operation of a combustion engine patented by Jean Joseph Etienne Lenoir in 1860 (Figs. 7.2 and 7.3). This idealised cycle is defined y three reversible
- A van der Waals gas is going through a Joule–Thomson process that keeps the enthalpy H constant. A van der Waals gas in characterised by the following equations of state,and the amount of gas is
- Heat pipes are devices used to transfer heat over a certain distance. A typical heat pipe looks like a metal rod, but modern versions, which are used for example to cool the hottest part of a phone,
- A container contains a substance in gaseous and liquid phases at room temperature (Fig. 6.16). The container is closed by a piston of surface area A, held back by a spring of elastic constant k. We
- A liquid is at equilibrium with its vapour. The vapour is assumed to be an ideal gas. The liquid has a molar latent heat of vaporisation ℓℓg that depends on temperature, with ℓℓg = A − BT,
- Water is cooled with ice cubes (Fig. 6.10). The water and the ice cubes are considered as an isolated system. Initially, the ice cubes are at melting temperature T0 and the water at temperature Ti.
- The infinitesimal heat transfer δQ is expressed as a function of the state variables T and V in equation (5.4). It was done as a function of the state variables T and p in equation (5.17). Express
- Determine the hydrostatic pressure p inside a droplet, as a function of its radius r (Fig. 4.11). Assume that the drop (d) forms at the end of a short thin tube mounted at the end of vertical
- An isolated system consists of two blocks made of the same substance (Fig. 3.9). The internal energies of blocks 1 and 2 are U1 = C1 T1 and U2 = C2 T2 where C1 and C2 are two positive constants. Two
- An isolated system consists of two subsystems labelled 1 and 2 analysed in exercise 3.6.1. Using the second law (2.2), show that in a stationary state when T1 > T2 the entropy production rate ΠS
- In exercise 3.6.2 devoted to the thermalisation of two blocks, show for the particular case where N1 = N2 = N that the entropy variation,is strictly positive.Data from exercise 3.6.2The entropy of a
- Model the rise of a balloon of mass M, which rises from the ground into the stratosphere [149]. At ground level, the balloon has a volume V0, which is much smaller than the volume Vmax it has when it
- A cylinder closed by a piston contains N moles of a diatomic gas characterised by U = (5/2) NRT and by pV = NRT, as in exercise 4.1. The gas has a temperature T when it is brought in contact with a
- This engine is operating a Rankine cycle on a biphasic fluid (Fig. 7.27). The cycle consists of five processes:Figure 7.27• 1→ 2: The fluid coming out of the turbine is completely condensed (1).
- A mixture of ice and water is heated up in such a way that the ice melts. The ice melts at a rate r and the molar latent heat of ice melting is ℓsℓ.a) Determine the thermal power PQ transferred
- The thermal response of a homogeneous system subjected to an infinitesimal heat transfer δQ is characterised by coefficients defined in equations (5.4) and (5.17) when either the state variables (T,
- An ideal gas undergoes a reversible adiabatic compression from an initial volume Vi and initial pressure pi to a final pressure pf. Determine the work Wif performed on the gas during this process.
- A gas container is thermally isolated except for a small hole that insures that the pressure inside the container is equal to the atmospheric pressure p0. Initially, the container holds Ni moles of
- A bicycle pump takes a volume ΔV of air at atmospheric pressure p0 and constant temperature T0 and compresses it so that it enters a tyre that has a volume V0. The air inside the tyre is initially
- A one-dimensional harmonic oscillator of mass M and spring constant k is subjected to a friction force Ff (t) = −λv (t) where v (t) is the velocity of the point mass and λ > 0. Using a
- Air is compressed inside the inner tube of a bike using a manual bicycle pump. The handle of the pump is brought down from an initial position x2 to a final position x1 where x12 and the norm of the
- In an experiment similar to the Joule experiment (Fig. 1.1), an electric motor is used instead of a weight to stir the liquid. The thermal power PQ, assumed to result from the friction, is known. The
- A mole of gas undergoes an expansion through two different processes. The gas satisfies the equation of state pV = NR T where R is a constant, N the number of moles, p the pressure, T the temperature
- Capilarity effects are taken into account by considering that the energy of the system contains contributions that are proportional to the surface area of the interfaces between the different parts
- A weight of mass M is hanging from a rope. The force F applied to the rope is such that the weight is lowered vertically at a velocity v, which may vary with time.a) Determine the expression for the
- A liquid is filling a container that has the form of a cone of angle α around a vertical axis (Fig. 1.9). The liquid enters the cone from the apex through a hole of diameter d at a velocity v (t) =
- A rubber cord of length L, which is a known state function L (T, F) of the temperature T of the cord and of the forces of magnitude F applied at each end to stretch it. Two physical properties of the
- A phase diagram is drawn for a mixture of two substances at a fixed pressure p with one liquid phase and two solid phases (Fig. 6.19). The substances are labelled 1 and 2 and the diagram is shown as
- A mole of oxygen, considered as a van der Waals gas, undergoes a reversible isothermal expansion at fixed temperature T0 from an initial volume Vi to a final volume Vf. Determine the work Wif
- A steel wire is wrapped over a block of ice with two heavy weights attached to the ends of the wire. The wire passes through a block of ice without cutting the block in two. The ice melts under the
- In a reactor of volume V0, initially empty, solid carbon is introduced in an excess amount together with NCO2(g) (0) moles of carbon dioxide. The reactor is brought to temperature T0 and the system
- A gas container of fixed volume V is divided into two compartments by an impermeable fixed wall. One compartment contains ideal gas 1, the other ideal gas 2. Both sides are at pressure p and
- We consider a substance that can be either in a gaseous phase inside a rigid container or in an absorbed phase on the surface of a substrate inside it. We analyse the equilibrium reached by the
- 1kg/s of nitrogen enters the turboexpander of a nitrogen liquefaction plant at 8 bar and 310 K with a velocity of 1.5 m/s and expands with pressure ratio of 6, exiting from the turbine with a
- Make a table like Table 1.1 for a Système Alternatif in which kG = 1 and the same primary quantities are used as in SI, choosing a suitable alias for each secondary quantity. What is kN in this
- An 80 kg student wishes to walk on snow without sinking and decides to make a pair of snow shoes. The student determined experimentally that the maximum pressure the snow can withstand is 0.6 kPa.
- Let Ѵ be the wind velocity approaching a windmill, D be the windmill rotor disk diameter, and ρ the air mass density. Show that the rate of kinetic energy flow through the windmill disk area is
- Let V be the water velocity in a river of width w and depth d, flowing along at a height h above a hydraulic power station. Show that the maximum electrical power that could be obtained by converting
- Calculate the power (MW) that could be obtained by converting the kinetic energy of the river water in Exercise 1.3 to electricity at 100% efficiency.Data From Exercise 1.3Let V be the water velocity
- Calculate the maximum energy (J) that could be obtained from 1 kg of water, assuming that the energy content of the mass, E = Mc2, could be completely converted to useful energy in some sort of
- Calculate the power requirements for lifting 40 kg sacks of cement up 1 m at the rate of 1 sack/second. If you had a team of superworkers who could do this all day long, how many would it take to
- A 5 kW electrical heater is left on for an hour and a half. Calculate the amount of energy transfer as heat from the heater to the room in terms of the following units: a) Unit for power in
- Determine the equivalents of 1 kg, 1 N, 1 J, and 1 W in a Système Deux in which both kN and kG are unity and the meter and the second are the primary units of length and time. Choose a suitable
- A home gas-fired heater has an output of 120,000 BTU/hr. The owner wants to exchange it with an electrical heater. What will be the equivalent electrical power in kW? Primary
- Determine the equivalents of 1 m, 1 kg, 1 N, 1 J, and 1 W in a Système Unis in which both kN and kG are unity, the speed of light is unity, and the second is the only primary unit. Choose a suitable
- 3 kg of ammonia at its critical state is placed in a constant-volume container, which is then cooled until the temperature is 300 K. How a much energy was transferred as heat from the ammonia in this
- A free-piston engine under development consists of a small piston in a cylinder. Each end of the cylinder behaves like a two-stroke engine, in which the following sequence of processes occurs
- An automobile engine has an output power of 120 HP. What is the equivalent motor power requirement in kW for an electric car?
- A simple piston–cylinder engine operates using a sequence of four processes:1-2 Compression at constant temperature, maintained by cooling.2-3 Heating at constant volume (by flames).3-4 Expansion
- A strong person might be able to lift a 110 lbf object up a distance of 5 ft in one second (at least once). What is the equivalent horsepower? What would be the average HP expenditure if the person
- The gas in an adiabatic piston–cylinder system undergoes a change of ΔU = −60 kJ during a process. How much was the energy transfer as work to or from the gas, and in which direction?
- A person in an elevator moving upward at 10 m/s lifts a 60 kg mass 1.5 m off the elevator floor in 2 s. How much work did the person do relative to the elevator? How much relative to the ground? Why
- What is the kinetic energy in J of a 2000 lbm car moving at 60 mph? Work out the answer first by starting with the expression for kinetic energy in the SI system, converting the basic data into SI
- How much energy transfer as work (J) is required to make fluid in an adiabatic container undergo a change ΔU = 200 kJ/kg?
- An open office room holds 50 employees, each dissipating 430 kJ of energy as heat per hour. In addition, twenty 80 W light bulbs are all left on at all times. Calculate how many 6 kW air-conditioning
- How much energy transfer as heat (J) is required to make fluid in a constant volume container undergo a change ΔU = 200 kJ/kg?
- Calculate the values of specific volume, specific internal energy, and specific enthalpy for water in vapor–liquid equilibrium at 180°C if its quality is 0.2. Use the tables in Appendix A.3 for
- Imagine turning the system of Exercise 2.13 vertically. Repeat the analysis, which now will involve the height of the piston. Using the same values as in Exercise 2.13(b), with D = 8 cm, plot the
- 2000 kg of oxygen is in a 1.8 m3 container maintained at 90 K. Calculate the liquid and vapor masses (kg) and the liquid and vapor volumes (m3). Use the tables in Appendix A.8 for data.Data From
- Consider the system in the figure below. Initially the gas in the cylinder is at high pressure Pi and the piston held in place at volume Vi with a lock. At time zero the lock is released and the gas
- Liquid oxygen (commonly referred to as LOX) in a rocket-propellant tank is kept at a pressure of approximately 1 bar. A certain ullage volume is occupied by saturated vapor for safety. Use the graph
- Initially 10 kg of saturated liquid water at 400 K and 2 kg of saturated water vapor at 300 K are together in a sealed, constant volume adiabatic container. After a time the water adjusts to a
- The gas in a piston–cylinder system undergoes a change of ΔU = 30 kJ during a process in which 40 kJ of energy as work are transferred from the gas to the piston. Was there energy transfer as heat
- Using the data of Appendix A.3, estimate β, κ, h, cν, and cp for H2O at 800 K and 1 bar.Data From Appendix A.3 T/ psat / MPa K v m³/kg 273.16 0.0006117 0.001000 206.0 0.0 0.0006985 0.001000 181.6
- In a constant-volume container, a fluid is to be heated so that its internal energy will change from 1200 kJ to 1600 kJ in 30 s. What is the power requirement (kW) of the electric heater?
- The temperature of 10 kg of air inside a piston–cylinder is increased from 25°C to 80°C using an electrical heater, while the pressure inside the cylinder is maintained constant. During this
- Calculate the density of gaseous H2O at each of the following states:a. 0.07 bar, 360 K,b. 1 atm, 700 K,c. 200 bar, 700 K,Using the perfect gas model. Compare the values obtained with the values
- In an adiabatic constant-volume container, a fluid is to be stirred mechanically with a motor providing 40 W of shaft power. How long can this go on if the internal energy of the fluid is not allowed
- Sketch on a P–ν diagram the process that the air inside a piston–cylinder undergoes during an isothermal (constant-temperature) expansion reducing the pressure by 300 kPa. Energy is then
- Consider the expansion of a gas at constant temperature in a water-cooled piston– cylinder system. The constant temperature is achieved by controlled input of energy as heat Q to the gas. Treating
- Consider the expansion of a gas at constant pressure in a water-cooled piston–cylinder system. The constant pressure is achieved by controlled input of energy as heat Q to the gas. Treating the gas
- A water cannon for rock cutting uses compressed gas to accelerate a 70 kg metal piston to 65 m/s. The energy of the piston is transferred to 0.9 kg of water, which is fired out of a small nozzle.
- A boiler is fed with 40 kg/s of water at a pressure of 100 bar and a temperature of 250°C. The velocity of the water at the inlet is negligible. The boiler delivers superheated steam with a pressure
- An inventor claims to have a solar powered heat pump that receives energy as heat from the sun at the rate of 10 kW and extracts energy as heat from the environment at the rate of 7 kW. This system
- A simple piston–cylinder engine operates using a sequence of three processes:1-2 Compression at constant temperature, maintained by heat transfer to the environment.2-3 Expansion at constant
- The motion actuator for a robotic manipulator consists of a simple piston–cylinder system where the pressure of the gas contained in the cylinder can be controlled by heating or cooling. The moving
- Technicians of a steam turbine manufacturing company have measured the following data for a simple 500 kW turbine:● Inlet state at T = 673 K and P = 40 bar, and● Outlet state at T = 378 K and P =
- Derive the expression for ln ϕ for a simple compressible fluid if the thermodynamic model is given as the non dimensional specific Helmholtz energy a(T, p) RT IG = = a¹G (t, 8) + a² {t,8).
- Sketch the u–T and v–T diagrams for H2O, showing lines of constant pressure. Indicate the saturated liquid and vapor lines.
- Estimate the temperature to which water at a the bottom of a 150 m deep lake would have to be raised before it would begin to boil.
- R134a flows in a pipe of a process plant at 3 m/s. Its pressure is 2 MPa and its temperature is 182°C. A plant component needs the working fluid at specific conditions. Design a steady-flow device
- A power plant operates between a hot reservoir consisting of a combustion chamber or a nuclear reactor and a cold reservoir consisting of the water of a river. It is modelled as a thermal machine
- Determine which of the following functions may represent the entropy of a system of positive temperature. In these expressions, E0 and V0 are constants representing an energy and a volume,
- Consider the function f (x, y) = y exp (ax)+xy+bx ln y where a and b are constants.a) Calculateb) Calculate 0f(x,y) Ox Of(x,y) ду and df(x,y)
- Two of the Massieu functions are functions of the following state variables:1.2.The Massieu functions are obtained by performing Legendre transformations of the state function entropy S (U, V) with
- An ideal gas is characterised by the relation pV = NRT where p is the pressure of the gas, V is the volume, T is the temperature, N is the number of moles of gas and R is a constant.a) Calculate the
- An ideal gas is characterised by the relation pV = NR T as in § 1.2 where the pressure p (T, V) is a function of T and V, the temperature T (p, V) is a function of p and V and the volume (T, p) is a
- A basin contains Ns (t) moles of salt dissolved in Nw (t) moles of water. The basin receives fresh water at a constant rate Ωin w. This water is assumed to be thoroughly mixed in the basin so that
- Rubbing hands together is a dissipative process that we would like to model and quantify.a) Determine the mechanical power PW dissipated by friction during this process, in terms of the friction
- Three processes are performed on a gas from a state given by (p1, V1) to a state given by (p2, V2) :a) An isochoric process followed by an isobaric process,b) An isobaric process followed by an
- A state of an elastic rod is described by the state variables entropy S and length L. The differential of the internal energy U(S, L) of the rod is written as,Note that f (S, L) has the units of a
- A Swiss watchmaker states in a flyer the mechanical power PW dissipated by a specific clock (Fig. 2.10). The work provided to the clock is due to the temperature Figure 2.10 A clock receives its
- A soap bubble is a system consisting of two subsystems. Subsystem (f) is the thin film and subsystem (g) is the gas enclosed inside the film. The surrounding air is a thermal bath. The equilibrium is
- Analyse the time evolution of a gas consisting of one substance that diffuses through a permeable wall. Thus, consider an isolated system containing N moles of gas, consisting of two subsystems of
- The entropy of a particular substance is given in terms of its internal energy U and number of moles N as [31],where R and E0 are positive constants. A system consists of two subsystems containing
- An isolated system of volume V0 consists of two subsystems, labelled 1 and 2, separated by an impermeable and moving diathermal wall of mass M and of negligible volume. Both subsystems contain a gas.
- Chemical Power An open system consists of a fluid of a single substance kept between two pistons sliding inside a cylinder with adiabatic walls. Matter enters and exits the cylinder in two specific
- Consider a cloud of droplets and assume that they all have the same diameter r. According to the Laplace formula (exercise 4.8), the pressure p (r) inside the droplets of radius r is related to the