Finally, if the second law of thermodynamics can be stated as the law of degradation of energy, then entropy can be regarded as the measure of the degree of energy degradation.
Problems
Engineering Mechanics
1 1.1 Determine the velocity required to keep satellite P in orbit at altitude S km above the surface of the earth. Force F2 is the balancing force that keeps the satellite in circular orbit. The gravitational force acting on the satellite, treated as a particle, is
2 1.2 A crank‐slider has a crank radius R = 100 mm, a connecting rod length L = 200 mm, and a crank angular speed ω = 100 rpm counterclockwise.Write the expressions for the displacement x and velocity of piston PDetermine the velocity when θ = 450.
3 1.3 Determine the moment of inertia and radius of gyration about an axis through the centre of a composite body with a central inner disk of mass 4 kg and radius 300 mm and a ring of mass 5 kg and radius 400 mm. The masses of the four spokes shown can be ignored.
4 1.4 A constant torque of 150 Nm applied to a turbine rotor is sufficient to overcome the constant bearing friction torque and give it a speed of 75 rpm from rest after 9 revolutions. When the 150 Nm torque is removed, the turbine rotor turns for a further 23 revolutions before stopping. Determine the moment of inertia of the rotor and the bearing friction torque.
5 1.5 A motor is required to reach an operating speed of 500 rpm in a time of 30 seconds from rest at a constant acceleration. DetermineThe required constant accelerationThe number of revolutions the motor turns to reach this operating speed. The motor is then turned off and comes to rest under a constant deceleration of 0.1 rad/s2 due to bearing friction. How long and how many revolutions does it take for the motor to come to reset?
Fluid Mechanics
1 1.6 The following nondimensional parameters are suggested for graphical representation of compressor characteristics:where is the mass flow rate, R is the gas constant, T is the gas temperature, D is the impeller diameter, and p is the gas pressure. Verify whether these parameters are truly nondimensional. If they are not, suggest a corrected form of the parameters.
2 1.7 Dimensional analysis has identified the following function for the pressure loss in a pipe:whereCheck if these two groups are nondimensional, and suggest remedies if they are not.Determine the actual correlation for flow of water in a 1500 mm long pipe with 12.5 mm diameter using experiments conducted at 20 °C with the following results:C, m/s0.3750.5940.8871.7803.3925.1577.1148.757Δp, Pa3007471 4805 07515 75332 60657 45682 832The water is at 20 °C, the density ρ = 998.2 kg/m3, and the dynamic viscosity is
3 1.8 Air is drawn into engine cylinder as the piston moves away from top dead centre (TDC) during the induction stroke, as shown in the following figure. Determine the pressure drop in the induction manifold for these conditions:Ambient pressure pa = 0.1 MPa.Flow velocity at the inlet Ca is negligible, and at the valve throat C = 56 m/s.Loss head at the valve restriction is given by hloss = βC2/2g, where the loss factor β = 7.Density of air ρa = 1.21 kg/m3. (Due to the small pressure drop during the induction process, air can be treated as incompressible fluid.)
4 1.9 In a frictionless cylinder and piston device, the piston is forced against a gas by a spring, which exerts a force directly proportional to the gas volume. In addition, the atmospheric pressure of 101.3 kPa acts on the outer face of the piston.Considering the gas as a system, calculate the work for the process from an initial state of 0.2 MPa, 0.1 m3 to final volume of 0.3 m3.If the spring is taken as a system, find the work for the same process.Explain the difference in work terms for the two systems in (a) and (b).
Thermodynamics
1 1.10 A gas mixture has the following molar (volume) composition:CO212.0%O24.0%N282.0%CO2.0%Determine the mixture mass composition.
2 1.11 The gravimetric analysis of a gaseous mixture shows the following components:H218.0%H2O4.0%O225.0%N221.0%CO3.0%CO213.0%CH416.0%What is the volumetric composition of the mixture?Calculate the specific gas constant and molecular mass of the mixture.
3 1.12 In a non‐flow process, there is a heat‐transfer loss of 1055 kJ and an internal energy increase of 210 kJ. Determine the work transfer, and state whether the process is an expansion or compression.
4 1.13 During the power stroke of an engine, the heat transferred to the cooling system was found to be 150 kJ/kg of working substance. The internal energy also decreased by 400 kJ/kg of working substance. Determine the work done, and state whether it is work done on the engine or by the engine.
5 1.14 The ventilation system servicing a lecture theatre seating 300 students suddenly fails. Assuming the average heat transfer rate from a person not actively working is about 400 kJ h−1,What is the change in internal energy of the air 15 minutes after shutdown?If all the students and the lecture theatre are taken to be the system, how much does the system's internal energy change?How do you account for the increase in air temperature?
6 1.15 The collecting panels of a small solar boiler receive radiation energy at the rate of 3400 kJ/m2 each hour during daylight. For a small rural power plant with 10 kW output, determine the required collector area if the electrical output is only 6% of the incident radiation.
7 1.16 In a steady‐flow open system, a fluid flows at the rate of 4 kg/s. It enters the system at a pressure of 600 kPa, a velocity of 220 m/s, internal energy 2200 kJ/kg, and specific volume 0.42 m3/kg. It leaves the system at a pressure of 150 kPa, velocity of 145 m/s, internal energy 1650 kJ/kg, and specific volume 1.5 m3/kg. During its passage through the system, the substance has a loss by heat transfer of 40 kJ/kg to the surroundings. Determine the power of the system, stating whether it is from or to the system. Neglect any change of gravitational potential energy.
8 1.17 Air enters a gas turbine system with a velocity of 105 m/s and has a specific volume of 0.8 m3/kg. The inlet area of the turbine is 0.05 m2. At exit, the air has a velocity of 135 m/s and specific volume of 1.5 m3/kg. In its passage through the turbine system, the specific enthalpy of the air is reduced by 145 kJ/kg and the air has a heat loss of 27 kJ/kg. DetermineThe mass flow rate of the air through the turbine systemThe exit area of the turbine system in m2The power developed by the turbine system in kilowatts
9 1.18 A 1.0 m3 closed vessel is filled with air at pressure p = 7 bar and temperature T = 288 K. The vessel is heated until the air temperature reaches 373 K. DetermineThe mass of air in the vesselThe air pressure at the end of the heating processThe change of internal energy, enthalpy, and entropy of air as a result of heating
10 1.19 A cylinder with a moving piston is filled with 2.5 kg of air. Initially, the pressure and temperature in the cylinder are, respectively, 0.8 MPa and 25 °C. If the air is heated to 100 °C at constant pressure, determineThe amount of heat inputWork doneChange of internal energy, enthalpy, and entropy of the airSpecific volume of the air at the start and end of the process.
11 1.20 0.1 kg of air in the cylinder of a compression ignition (CI) engine undergoes polytropic compression during which the volume decrease 16 times and the pressure increases 45 times. If the initial temperature is 320 K, determineThe polytropic index of the compression processTemperature of the air at the end of compressionCompression workChange of internal energy, enthalpy ant entropyHeat added to the process
12 1.21 1.0 kg of air undergoes a Carnot cycle in which the heat source is at 900 K and the heat sink at 300 K. if the minimum and maximum pressures in the cycle are 0.1 and 6.0 MPa, respectively, determineProperties at the characteristic pointsWork doneThermodynamic efficiency
13 1.22
