Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions

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A steam engine is to have its thermal efficiency improved from 8.00% to 10.0% while continuing to pro-duce 4500 J of useful work each cycle. (a) Does the ratio of the heat output to heat input (1) increase, (2) remain the same, or (3) decrease? Why? (b) What is the change in Qc/Qh in this example?
An engineer redesigns a heat engine and improves its thermal efficiency from 20% to 25%. (a) Does the ratio of the heat input to heat output (1) increase, (2) remain the same, or (3) decrease? Explain. (b) What is the engine’s change in Qh/Qc?
An ideal gas goes through a thermodynamic process in which 500 J of work is done on the gas and the gas loses 300 J of heat. What is the change in internal energy of the gas?
When running, a refrigerator exhausts heat to the kitchen at a rate of 10 kW when the required input work is done at a rate of 3.0 kW. (a) At what rate is heat removed from its cold interior? (b) What is the COP of the refrigerator?
A refrigerator with a COP of 2.2 removes 4.2 x 105 J of heat from its interior each cycle. (a) How much heat is exhausted each cycle? (b) What is the total work input in joules for 10 cycles?
An air conditioner has a COP of 2.75. What is the power rating of the unit if it is to remove 1.00 x 107 J of heat from a house interior in 20 min?
A heat pump removes 2.2 x 103 J of heat from the outdoors and delivers 1.3 x 103J of heat to the inside of a house each cycle. (a) How much work is required per cycle? (b) What is the COP of this pump?
A steam engine has a thermal efficiency of 15.0%. If its heat input for each cycle is supplied by the condensation of 8.00 kg of steam at 100 oC. (a) What is the net work output per cycle, and (b) How much heat is lost to the surroundings in each cycle?
A coal-fired power plant produces 900 MW of electric power and operates at a thermal efficiency of 25% (a) What is the input heat rate from the burning coal? (b) What is the rate of heat discharge from the plant? (c) Water at from a nearby river is used to cool the discharged heat. If the cooling
A gasoline engine has a thermal efficiency of 25.0%. If heat is expelled from the engine at a rate of 1.50 x 106 J/h, how long does the engine take to perform a task that requires an amount of work of 1.5 x 106 J?
A four-stroke engine runs on the Otto cycle. It delivers 150 hp at 3600 rpm. (a) How many cycles are in 1 min? (b) If the thermal efficiency of the engine is 20%, what is the heat input per minute? (c) How much heat is wasted (per minute) to the environment?
A Carnot engine has an efficiency of 30% and takes in heat from a high-temperature reservoir at 178 oC. What is the Celsius temperature of the engine’s low-temperature reservoir?
A steam engine operates between 100 oC and 20 oC. What is the Carnot efficiency of the ideal engine that operates between these temperatures?
While doing 500 J of work, an ideal gas expands adiabatically to 1.5 times its initial volume. (a) The temperature of the gas (1) increases, (2) remains the same, (3) decreases. Why? (b) What is the change in the internal energy of the gas?
It has been proposed that temperature differences in the ocean could be used to run a heat engine to generate electricity. In tropical regions, the water temperature is about 25oC at the surface and about 5 oC at very deep depths. (a) What would be the maximum theoretical efficiency of such an
What is the Celsius temperature of the hot reservoir of a Carnot engine that is 32% efficient and has a 20 oC cold reservoir?
An engineer wants to run a heat engine with an efficiency of 40% between a high-temperature reservoir at 300 oC and a low-temperature reservoir. What is the maximum Celsius temperature of the low-temperature reservoir?
A Carnot engine with an efficiency of 40% operates with a low-temperature reservoir at 40 oC and exhausts 1200 J of heat each cycle. What are (a) The heat input per cycle and (b) The Celsius temperature of the high-temperature reservoir?
A Carnot engine takes 2.7 x 104J of heat per cycle from a high-temperature reservoir at 320 oC and exhausts some of it to a low-temperature reservoir at 120 oC. How much net work is done by the engine per cycle?
A Carnot engine takes in heat from a reservoir at 350 oC and has an efficiency of 35%. The exhaust temperature is not changed and the efficiency is increased to 40%, (a) The temperature of the hot reservoir is (1) lower than (2) equal to, (3) higher than 350 oC. Explain. (b) What is the new
An inventor claims to have created a heat engine that produces 10.0 kW of power for a 15.0-kW heat input while operating between reservoirs at 27 oC and 427 oC. (a) Is this claim valid? (b) To produce 10.0 kW of power, what is the minimum heat input required?
An inventor claims to have developed a heat engine that, each cycle, takes in 5.0 x 105J of heat from a high-temperature reservoir at 400 oC and exhausts 2.0 x 105J to the surroundings at 125 oC. Would you invest your money in the production of this engine? Explain.
A heat engine operates at a thermal efficiency that is 45% of the Carnot efficiency. If the temperatures of the high-temperature and low-temperature reservoirs are 400 oC and 50 oC, respectively, what are the Carnot efficiency and the thermal efficiency of the engine?
A heat engine’s thermal efficiency is of the Carnot efficiency of an engine operating between temperatures of 80oC and 375oC. (a) What is the Carnot efficiency of the heat engine? (b) If the heat engine absorbs heat at a rate of 50 kW, at what rate is heat exhausted?
An ideal gas expands from 1.0 m3 to 3.0 m3 at atmospheric pressure while absorbing of heat in the process. (a) The temperature of the system (1) increases, (2) stays the same, (3) decreases. Explain. (b) What is the change in internal energy of the system?
In each cycle, a Carnot engine takes 800 J of heat from a high-temperature reservoir and discharges 600 J to a low-temperature reservoir. What is the ratio of the temperature of the high-temperature reservoir to that of the low-temperature reservoir?
A Carnot engine operating between reservoirs at 27oC and 227oC does 1500 J of work in each cycle. (a) The change in entropy for the engine for each cycle is (1) negative, (2) zero, (3) positive. Why? (b) What is the heat input of the engine?
The autoignition temperature of a fuel is defined as the temperature at which a fuel–air mixture would self-explode and ignite. Thus, it sets an upper limit on the temperature of the hot reservoir in an automobile engine. The autoignition temperatures for commonly available gasoline and diesel
Because of limitations on materials, the maximum temperature of the superheated steam used in a turbine for the generation of electricity is about 450 oC. (a) If the steam condenser operates at 20 oC, what is the maxi-mum Carnot efficiency of a steam turbine generator? (b) The actual efficiency
The working substance of a cyclic heat engine is 0.75 kg of an ideal gas. The cycle consists of two isobaric processes and two isometric processes, as shown in Fig. 12.26. What would be the efficiency of a Carnot engine operating with the same high-temperature and low-temperature reservoirs?
Equation 12.15 shows that the greater the temperature difference between the reservoirs of a heat engine, the greater the engine’s Carnot efficiency. Suppose you had the choice of raising the temperature of the high-temperature reservoir by a certain number of kelvins or lowering the temperature
There is a Carnot coefficient of performance (COPC) for an ideal, or Carnot, refrigerator.(a) Show that this quantity is given by(b) What does this tell you about adjusting the temperatures for the maximum COP of a refrigerator? (Can you guess the equation for the COPC for a heat pump?)
A salesperson tells you that a new refrigerator with a high COP removes 2.6 x 103J (each cycle) from the inside of the refrigerator at 5.0 oC and expels 2.8 x 103J into the 30oC kitchen. (a) What is the refrigerator’s COP? (b) Is this scenario possible? Justify your answer.
An ideal heat pump is equivalent to a Carnot engine running in reverse. (a) Show that the Carnot COP of the heat pump is COPC = 1/εC where εC is the Carnot efficiency of the heat engine. (b) If a Carnot engine has an efficiency of 40%, what would be the COPC when it runs in reverse as a heat
A heat engine with a thermal efficiency of 25% is used to hoist 2.5-kg bricks to an elevation of 3.0 m. If the engine expels heat to the environment at a rate of 1.2 x 106 J/h, how many bricks can the engine hoist in 2.0 h?
An ideal gas is under an initial pressure of 2.45 x 104 Pa and occupies a volume of 0.20 m3. The slow addition of 8.4 x 103 J of heat to this gas causes it to expand isobarically to a volume of 0.40 m3. (a) How much work is done by the gas in the process? (b) Does the internal energy of the gas
When cruising at 75 mi/h on a highway, a car’s engine develops 45 hp. If this engine has a thermodynamic efficiency of and 1 gal of gasoline has an energy content of 1.3 x 108J, what is the fuel efficiency (in miles per gallon) of this car?
A gram of water (volume of 1.00 cm3) at 100 oC is converted to 1.67 x 103cm3 of steam at atmospheric pres-sure. What is the change in the internal energy of the water (steam)?
In a highly competitive game, a basketball player can produce 300 W of power. Assuming the efficiency of the player’s “engine” is 15% and heat dissipates primarily through the evaporation of perspiration, what mass of perspiration is evaporated per hour?
A Carnot engine is to produce 100 J of work per cycle. If 300 J of heat is exhausted to a 27oC cold reservoir per cycle, what is the change in entropy of the hot reservoir per cycle?
A quantity of an ideal gas at an initial pressure of 2.00 atm undergoes an adiabatic expansion to atmospheric pressure. What is the ratio of the final temperature to the initial temperature of the gas?
A 100-MW power generating plant has an efficiency of 40%. If water is used to carry off the wasted heat and the temperature of the water is not to increase by more than 10 oC, what mass of water must flow through the plant each second?
An ice machine is to convert 10oC water to 0oC ice. If the machine has a COP of 2.0 and consumes electrical power at a rate of 1.0 kW, how much ice can it make in 1.0 h?
An Olympic weight lifter lifts 145 kg a vertical distance of 2.1 m. When he does so, 6.0 x 104 J of heat is transferred to air through perspiration. Does he gain or lose internal energy and how much?
An ideal gas is taken through the reversible processes shown in Fig. 12.21.(a) Is the overall change in the internal energy of the gas (1) positive, (2) zero, or (3) negative? Explain. (b) In terms of state variables p and V, how much work is done by or on the gas, and (c) What is the net heat
Make a control volume around the turbine in the steam power plant in Fig. 1.1 and list the flows of mass and energy that are there.
Density of fibers, rock wool insulation, foams and cotton is fairly low. Why is that?
How much mass is there approximately in 1 L of mercury (Hg)? Atmospheric air?
Can you carry 1 m3 of liquid water?
A manometer shows a pressure difference of 1 m of liquid mercury. Find ΔP in kPa.
You dive 5 m down in the ocean. What is the absolute pressure there?
What pressure difference does a 10 m column of atmospheric air show?
The pressure at the bottom of a swimming pool is evenly distributed. Suppose we look at a cast iron plate of 7272 kg lying on the ground with an area of 100 m2. What is the average pressure below that? Is it just as evenly distributed?
A laboratory room keeps a vacuum of 0.1 kPa. What net force does that put on the door of size 2 m by 1 m?
A tornado rips off a 100 m2 roof with a mass of 1000 kg. What is the minimum vacuum pressure needed to do that if we neglect the anchoring forces?
What is a temperature of –5oC in degrees Kelvin?
Make a control volume around the whole power plant in Figure 1.2 and with the help of Fig. 1.1 list what flows of mass and energy are in or out and any storage of energy. Make sure you know what is inside and what is outside your chosen C.V.
What is the smallest temperature in degrees Celsuis you can have? Kelvin?
Density of liquid water is ρ = 1008 – T/2 [kg/m3] with T in oC. If the temperature increases 10oC how much deeper does a 1 m layer of water become?
Convert the formula for water density in problem 21 to be for T in degrees Kelvin.
A steel cylinder of mass 2 kg contains 4 L of liquid water at 25oC at 200 kPa. Find the total mass and volume of the system. List two extensive and three intensive properties of the water.
An apple “weighs” 80 g and has a volume of 100 cm3 in a refrigerator at 8oC. What is the apple density? List three intensive and two extensive properties of the apple.
One kilopond (1 kp) is the weight of 1 kg in the standard gravitational field. How many Newtons (N) is that?
A pressurized steel bottle is charged with 5 kg of oxygen gas and 7 kg of nitrogen gas. How many kmoles are in the bottle?
The “standard” acceleration (at sea level and 45° latitude) due to gravity is 9.80665 m/s2. What is the force needed to hold a mass of 2 kg at rest in this gravitational field? How much mass can a force of 1 N support?
A force of 125 N is applied to a mass of 12 kg in addition to the standard gravitation. If the direction of the force is vertical up find the acceleration of the mass.
A model car rolls down an incline with a slope so the gravitational “pull” in the direction of motion is one third of the standard gravitational force (see Problem 2.1). If the car has a mass of 0.45 kg find the acceleration.
Make a control volume that includes the steam flow around in the main turbine loop in the nuclear propulsion system in Fig.1.3. Identify mass flows (hot or cold) and energy transfers that enter or leave the C.V.
When you move up from the surface of the earth the gravitation is reduced as g = 9.807 − 3.32 × 10-6 z, with z as the elevation in meters. How many percent is the weight of an airplane reduced when it cruises at 11 000 m?
A car drives at 60 km/h and is brought to a full stop with constant deceleration in 5 seconds. If the total car and driver mass is 1075 kg find the necessary force.
A car of mass 1775 kg travels with a velocity of 100 km/h. Find the kinetic energy. How high should it be lifted in the standard gravitational field to have a potential energy that equals the kinetic energy?
A 1200-kg car moving at 20 km/h is accelerated at a constant rate of 4 m/s2 up to a speed of 75 km/h. What are the force and total time required?
A steel plate of 950 kg accelerates from rest with 3 m/s2 for a period of 10s. What force is needed and what is the final velocity?
A 15 kg steel container has 1.75 kilomoles of liquid propane inside. A force of 2 kN now accelerates this system. What is the acceleration?
A bucket of concrete of total mass 200 kg is raised by a crane with an acceleration of 2 m/s2 relative to the ground at a location where the local gravitational acceleration is 9.5 m/s2. Find the required force.
On the moon the gravitational acceleration is approximately one-sixth that on the surface of the earth. A 5-kg mass is “weighed” with a beam balance on the surface on the moon. What is the expected reading? If this mass is weighed with a spring scale that reads correctly for standard gravity on
A 5 m3 container is filled with 900 kg of granite (density 2400 kg/m3) and the rest of the volume is air with density 1.15 kg/m3. Find the mass of air and the overall (average) specific volume.
A tank has two rooms separated by a membrane. Room A has 1 kg air and volume 0.5 m3, room B has 0.75 m3 air with density 0.8 kg/m3. The membrane is broken and the air comes to a uniform state. Find the final density of the air.
Take a control volume around your kitchen refrigerator and indicate where the components shown in Figure 1.6 are located and show all flows of energy transfer.
A 1 m3 container is filled with 400 kg of granite stone, 200 kg dry sand and 0.2 m3 of liquid 25°C water. Use properties from tables A.3 and A.4. Find the average specific volume and density of the masses when you exclude air mass and volume.
A 1 m3 container is filled with 400 kg of granite stone, 200 kg dry sand and 0.2 m3 of liquid 25°C water. Use properties from tables A.3 and A.4 and use air density of 1.1 kg/m3. Find the average specific volume and density of the 1 m3 volume.
One kilogram of diatomic oxygen (O2 molecular weight 32) is contained in a 500-L tank. Find the specific volume on both a mass and mole basis (v and ).
A 15-kg steel gas tank holds 300 L of liquid gasoline, having a density of 800 kg/m3. If the system is decelerated with 6 m/s2 what is the needed force?
A hydraulic lift has a maximum fluid pressure of 500 kPa. What should the piston-cylinder diameter be so it can lift a mass of 850 kg?
A piston/cylinder with cross sectional area of 0.01 m2 has a piston mass of 100 kg resting on the stops, as shown in Fig. P2.45. With an outside atmospheric pressure of 100 kPa, what should the water pressure be to lift the piston?
A vertical hydraulic cylinder has a 125-mm diameter piston with hydraulic fluid inside the cylinder and an ambient pressure of 1 bar. Assuming standard gravity, find the piston mass that will create a pressure inside of 1500 kPa.
A valve in a cylinder has a cross sectional area of 11 cm2 with a pressure of 735 kPa inside the cylinder and 99 kPa outside. How large a force is needed to open the valve?
A cannon-ball of 5 kg acts as a piston in a cylinder of 0.15 m diameter. As the gun-powder is burned a pressure of 7 MPa is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally?
Repeat the previous problem for a cylinder (cannon) pointing 40 degrees up relative to the horizontal direction.
An electric dip heater is put into a cup of water and heats it from 20oC to 80oC. Show the energy flow(s) and storage and explain what changes.
A large exhaust fan in a laboratory room keeps the pressure inside at 10 cm water relative vacuum to the hallway. What is the net force on the door measuring 1.9 m by 1.1 m?
What is the pressure at the bottom of a 5 m tall column of fluid with atmospheric pressure 101 kPa on the top surface if the fluid is a) Water at 20°C b) Glycerine 25°C c) Light oil
The hydraulic lift in an auto-repair shop has a cylinder diameter of 0.2 m. To what pressure should the hydraulic fluid be pumped to lift 40 kg of piston/arms and 700 kg of a car?
A 2.5 m tall steel cylinder has a cross sectional area of 1.5 m2. At the bottom with a height of 0.5 m is liquid water on top of which is a 1 m high layer of gasoline. The gasoline surface is exposed to atmospheric air at 101 kPa. What is the highest pressure in the water?
At the beach, atmospheric pressure is 1025 mbar. You dive 15 m down in the ocean and you later climb a hill up to 250 m elevation. Assume the density of water is about 1000 kg/m3 and the density of air is 1.18 kg/m3. What pressure do you feel at each place?
A piston, mp = 5 kg, is fitted in a cylinder, A = 15 cm2, that contains a gas. The setup is in a centrifuge that creates an acceleration of 25 m/s2 in the direction of piston motion towards the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
A steel tank of cross sectional area 3 m2 and 16 m tall weighs 10 000 kg and it is open at the top. We want to float it in the ocean so it sticks 10 m straight down by pouring concrete into the bottom of it. How much concrete should I put in?
Liquid water with density ρ is filled on top of a thin piston in a cylinder with cross-sectional area A and total height H. Air is let in under the piston so it pushes up, spilling the water over the edge. Deduce the formula for the air pressure as a function of the piston elevation from the
The density of atmospheric air is about 1.15 kg/m3, which we assume is constant. How large an absolute pressure will a pilot see when flying 1500 m above ground level where the pressure is 101 kPa.
A differential pressure gauge mounted on a vessel shows 1.25 MPa and a local barometer gives atmospheric pressure as 0.96 bar. Find the absolute pressure inside the vessel.

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Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions

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