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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A Carnot refrigerator operates between reservoirs at -20°C and 50°C in a 25°C room. The refrigerator is a 40 cm × 40 cm × 40 cm box. Five of the walls are perfect insulators, but the sixth is a
Prove that the work done in an adiabatic process i → f is Ws = (pfVf - piVi)/(1 - ϒ).
A heat engine with 50% of the Carnot efficiency operates between reservoirs at 20°C and 200°C. The engine inputs heat energy at an average rate of 63 W while compressing a spring 22 cm in 0.50 s.
The engine that powers a crane burns fuel at a flame temperature of 2000°C. It is cooled by 20°C air. The crane lifts a 2000 kg steel girder 30 m upward. How much heat energy is transferred to the
FIGURE P21.35 shows a heat engine going through one cycle.The gas is diatomic. The masses are such that when the pin is removed, in steps 3 and 6, the piston does not move.a. Draw the pV diagram for
A Carnot heat engine with thermal efficiency 1/3 is run backward as a Carnot refrigerator. What is the refrigerator’s coefficient of performance?
The coefficient of performance of a refrigerator is 5.0. The compressor uses 10 J of energy per cycle.a. How much heat energy is exhausted per cycle?b. If the hot-reservoir temperature is 27°C, what
A Carnot refrigerator operating between -20°C and +20°C extracts heat from the cold reservoir at the rate 200 J/s. What are(a) The coefficient of performance of this refrigerator,(b) The rate at
A heat engine operating between a hot reservoir at 500°C and a cold reservoir at 0°C is 60% as efficient as a Carnot engine. If this heat engine and the Carnot engine do the same amount of work,
A heat engine operating between energy reservoirs at 20°C and 600°C has 30% of the maximum possible efficiency. How much energy must this engine extract from the hot reservoir to do 1000 J of work?
The ideal gas in a Carnot engine extracts 1000 J of heat energy during the isothermal expansion at 300°C. How much heat energy is exhausted during the isothermal compression at 50°C?
A Carnot engine whose hot-reservoir temperature is 400°C has a thermal efficiency of 40%. By how many degrees should the temperature of the cold reservoir be decreased to raise the engine’s
A Carnot engine operating between energy reservoirs at temperatures 300 K and 500 K produces a power output of 1000 W.What are(a) The thermal efficiency of this engine,(b) The rate of heat input, in
a. A heat engine does 200 J of work per cycle while exhausting 600 J of heat to the cold reservoir. What is the engine’s thermal efficiency?b. A Carnot engine with a hot-reservoir temperature of
A heat engine does 10 J of work and exhausts 15 J of waste heat during each cycle.a. What is the engine’s thermal efficiency?b. If the cold-reservoir temperature is 20°C, what is the minimum
At what cold-reservoir temperature (in °C) would a Carnot engine with a hot-reservoir temperature of 427°C have an efficiency of 60%?
Which, if any, of the refrigerators in FIGURE EX21.23 violate (a) The first law of thermodynamics(b) The second law of thermodynamics? Explain. (a) Hot reservoir (Ь) Hot reservoir TH 3 400 K TH
Which, if any, of the heat engines in FIGURE EX21.22 violate (a) The first law of thermodynamics(b) The second law of thermodynamics? Explain.a.b.c. Hot reservoir T = 600 K 500 J Heat 300 J
An air conditioner removes 5.0 × 105 J/min of heat from a house and exhausts 8.0 × 105 J/min to the hot outdoors.a. How much power does the air conditioner’s compressor require?b. What is the air
What are(a) The heat extracted from the cold reservoir(b) The coefficient of performance for the refrigerator shown in FIGURE EX21.20? 105 J- W, =-119 J Adiabats W, = 78 J
The coefficient of performance of a refrigerator is 6.0. The refrigerator’s compressor uses 115 W of electric power and is 95% efficient at converting electric power into work. What are (a)
At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of 50%?
A heat engine uses a diatomic gas in a Brayton cycle. What is the engine’s thermal efficiency if the gas volume is halved during the adiabatic compression?
How much heat is exhausted to the cold reservoir by the heat engine shown in FIGURE EX21.16? p (kPa) 225 J 300- 200- 90 J 100- V (cm') 0+ 300 600 FIGURE EX21.16
What are(a) The thermal efficiency(b) The heat extracted from the hot reservoir for the heat engine shown in FIGURE EX21.15? p (kPa) 300 180 J 200 100- 100 J V (cm) 600 200 400 FIGURE EX21.15
What are(a) Wout and QH(b) The thermal efficiency for the heat engine shown in FIGURE EX21.14? P (kPa) 400 - 200 - 114 J V(cm) 0+ 100 200 FIGURE EX21.14
What are(a) Wout and QH(b) The thermal efficiency for the heat engine shown in FIGURE EX21.13? p (kPa) 400 Q = -90 J 200 Q =-25 J V (cm) 0- 100 200 FIGURE EX21.13
A gas following the pV trajectory of FIGURE EX21.12 does 60 J of work per cycle. What is pmax? P (kPa) Pmax 100 - V (cm) 0+ O 200 400 600 800 FIGURE EX21.12
How much work is done per cycle by a gas following the pV trajectory of FIGURE EX21.11? p (atm) 3- 2- 1- V (cm³) 600 0+ 200 400 FIGURE EX21.11
The first and second laws of thermodynamics are sometimes stated as “You can’t win” and “You can’t even break even.” Do these sayings accurately characterize the laws of thermodynamics as
The cycle of FIGURE EX21.10 consists of four processes. Make a table with rows labeled A to D and columns labeled Î”Eth, Ws, and Q. Fill each box in the table with +, -, or 0 to indicate
It gets pretty hot in your apartment. In browsing the Internet, you find a company selling small “room air conditioners.” You place the air conditioner on the floor, plug it in, and—the
The cycle of FIGURE EX21.9 consists of three processes. Make a table with rows labeled A€“C and columns labeled Î”Eth, Ws, and Q. Fill each box in the table with +, -, or 0 to
Do the energy-transfer diagrams in FIGURE Q21.9 represent possible refrigerators? If not, what is wrong?a.b.c. Hot reservoir 600 K 10 J 20 J |10 J 300 K Cold reservoir Hot reservoir 600 K 30 J 20 J
1.0 L of 20°C water is placed in a refrigerator. The refrigerator’s motor must supply an extra 8.0 W of power to chill the water to 5°C in 1.0 h. What is the refrigerator’s coefficient of
Do the energy-transfer diagrams in FIGURE Q21.8 represent possible heat engines? If not, what is wrong?a.b.c. Hot reservoir 600 K 10 J 10 J 300 K Cold reservoir Hot reservoir 600 K 10 J 6J 300 K
The power output of a car engine running at 2400 rpm is 500 kW. How much(a) Work is done(b) Heat is exhausted per cycle if the engine’s thermal efficiency is 20%? Give your answers in kJ.
A heat engine satisfies Wout = Qnet. Why is there no ΔEth term in this relationship?
A 32%-efficient electric power plant produces 900 MW of electric power and discharges waste heat into 20°C ocean water.Suppose the waste heat could be used to heat homes during the winter instead of
FIGURE Q21.6 shows the thermodynamic cycles of two heat engines. Which heat engine has the larger thermal efficiency? Or are they the same? Explain. Engine 1 Engine 2 Pi P1- P2- P2- - V V2 v, V, V2
A refrigerator requires 200 J of work and exhausts 600 J of heat per cycle. What is the refrigerator’s coefficient of performance?
Rank in order, from largest to smallest, the thermal efficiencies η1to η4of the four heat engines in FIGURE Q21.5. Explain. Hot reservoir Hot reservoir 10 J 100 J 4 J 2 40 J 6J 60 J Cold reservoir
50 J of work are done per cycle on a refrigerator with a coefficient of performance of 4.0. How much heat is(a) Extracted from the cold reservoir(b) Exhausted to the hot reservoir per cycle?
FIGURE Q21.4 shows the pV diagram of a heat engine. During which stage or stages is (a) Heat added to the gas, (b) Heat removed from the gas, (c) Work done on the gas, (d) Work done by the gas? P2-
A heat engine extracts 55 kJ of heat from the hot reservoir each cycle and exhausts 40 kJ of heat. What are(a) The thermal efficiency(b) The work done per cycle?
Could you have a heat engine with η > 1? Explain.
A heat engine with a thermal efficiency of 40% does 100 J of work per cycle. How much heat is(a) Extracted from the hot reservoir(b) Exhausted to the cold reservoir per cycle?
A heat engine does 200 J of work per cycle while exhausting 400 J of waste heat. What is the engine’s thermal efficiency?
An experiment you’re designing needs a gas with ϒ = 1.50.You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with ϒ = 1.50
n1 moles of a monatomic gas and n2 moles of a diatomic gas are mixed together in a container.a. Derive an expression for the molar specific heat at constant volume of the mixture.b. Show that your
The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick.
A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not?a. The
In the discussion following Equation 20.43 it was said that Q1 = -Q2. Prove that this is so.
A monatomic gas and a diatomic gas have equal numbers of moles and equal temperatures. Both are heated at constant pressure until their volume doubles. What is the ratio Qdiatomic /Qmonatomic?
A water molecule has its three atoms arranged in a “V” shape, so it has rotational kinetic energy around any of three mutually perpendicular axes. However, like diatomic molecules, its
Scientists studying the behavior of hydrogen at low temperatures need to lower the temperature of 0.50 mol of hydrogen gas from 300 K to 30 K. How much thermal energy must they remove from the gas?
5.0 × 1023 nitrogen molecules collide with a 10 cm2 wall each second. Assume that the molecules all travel with a speed of 400 m/s and strike the wall head-on. What is the pressure on the wall?
On earth, STP is based on the average atmospheric pressure at the surface and on a phase change of water that occurs at an easily produced temperature, being only slightly cooler than the average air
Uranium has two naturally occurring isotopes. 238U has a natural abundance of 99.3% and 235U has an abundance of 0.7%.It is the rarer 235U that is needed for nuclear reactors. The isotopes are
Equation 20.3 is the mean free path of a particle through a gas of identical particles of equal radius. An electron can be thought of as a point particle with zero radius.a. Find an expression for
a. Find an expression for the vrms of gas molecules in terms of p, V, and the total mass of the gas M.b. A gas cylinder has a piston at one end that is moving outward at speed vpiston during an
You are watching a science fiction movie in which the hero shrinks down to the size of an atom and fights villains while jumping from air molecule to air molecule. In one scene, the hero’s molecule
Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H2). The number density is about 1 atom/cm3 and the temperature is about 3 K.a. Estimate the
Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean free path of photons through the gas. Photons are not gas molecules, so the mean free
A mad engineer builds a cube, 2.5 m on a side, in which 6.2 cm-diameter rubber balls are constantly sent flying in random directions by vibrating walls. He will award a prize to anyone who can figure
Dust particles are ≈ 10 mm in diameter. They are pulverized rock, with ρ ≈ 2500 kg/m3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 20°C?
From what height must an oxygen molecule fall in a vacuum so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 300 K?
The pressure inside a tank of neon is 150 atm. The temperature is 25°C. On average, how many atomic diameters does a neon atom move between collisions?
Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container.After a long time has passed, you record the number of balls in each
4.0 mol of monatomic gas A interacts with 3.0 mol of monatomic gas B. Gas A initially has 9000 J of thermal energy, but in the process of coming to thermal equilibrium it transfers 1000 J of heat
2.0 mol of monatomic gas A initially has 5000 J of thermal energy.It interacts with 3.0 mol of monatomic gas B, which initially has 8000 J of thermal energy.a. Which gas has the higher initial
A rigid container holds 0.20 g of hydrogen gas. How much heat is needed to change the temperature of the gasa. From 50 K to 100 K?b. From 250 K to 300 K?c. From 2250 K to 2300 K?
A cylinder of nitrogen gas has a volume of 15,000 cm3 and a pressure of 100 atm.a. What is the thermal energy of this gas at room temperature (20°C)?b. What is the mean free path in the gas?c. The
1.0 mol of a monatomic gas interacts thermally with 1.0 mol of an elemental solid. The gas temperature decreases by 50°C at constant volume. What is the temperature change of the solid?
What is the thermal energy of 100 cm3 of aluminum at 100°C?
The thermal energy of 1.0 mol of a substance is increased by 1.0 J. What is the temperature change if the system is(a) A monatomic gas,(b) A diatomic gas,(c) A solid?
A 6.0 m × 8.0 m × 3.0 m room contains air at 20°C. What is the room’s thermal energy?
The rms speed of the atoms in a 2.0 g sample of helium gas is 700 m/s. What is the thermal energy of the gas?
A 10 g sample of neon gas has 1700 J of thermal energy. Estimate the average speed of a neon atom.
The atmosphere of the sun consists mostly of hydrogen atoms (not molecules) at a temperature of 6000 K. What are(a) The average translational kinetic energy per atom(b) The rms speed of the atoms?
What are(a) The average kinetic energy(b) The rms speed of a proton in the center of the sun, where the temperature is 2.0 × 107 K?
During a physics experiment, helium gas is cooled to a temperature of 10 K at a pressure of 0.10 atm. What are(a) The mean free path in the gas,(b) The rms speed of the atoms,(c) The average energy
Suppose you double the temperature of a gas at constant volume. Do the following change? If so, by what factor?a. The average translational kinetic energy of a molecule.b. The rms speed of a
At STP, what is the total translational kinetic energy of the molecules in 1.0 mol of(a) Hydrogen,(b) Helium,(c) Oxygen?
Atoms can be “cooled” to incredibly low temperatures by letting them interact with a laser beam. Various novel quantum phenomena appear at these temperatures. What is the rms speed of cesium
By what factor does the rms speed of a molecule change if the temperature is increased from 10°C to 1000°C?
The rms speed of molecules in a gas is 600 m/s. What will be the rms speed if the gas pressure and volume are both halved?
At what temperature (in °C) do hydrogen molecules have the same rms speed as nitrogen molecules at 100°C?
1.5 m/s is a typical walking speed. At what temperature (in °C) would nitrogen molecules have an rms speed of 1.5 m/s?
What are the rms speeds of(a) Argon atoms(b) Hydrogen molecules at 800°C?
A gas consists of a mixture of neon and argon. The rms speed of the neon atoms is 400 m/s. What is the rms speed of the argon atoms?
A cylinder contains gas at a pressure of 2.0 atm and a number density of 4.2 × 1025 m-3. The rms speed of the atoms is 660 m/s. Identify the gas.
At 100°C the rms speed of nitrogen molecules is 576 m/s.Nitrogen at 100°C and a pressure of 2.0 atm is held in a container with a 10 cm × 10 cm square wall. Estimate the rate of molecular
The number density in a container of neon gas is 5.00 × 1025 m-3. The atoms are moving with an rms speed of 660 m/s. What are(a) The temperature(b) The pressure inside the container?
FIGURE EX20.10 is a histogram showing the speeds of the molecules in a very small gas. What are (a) The most probable speed, (b) The average speed, (c) The rms speed? N In. 3- 2- -v (m/s) FIGURE
Eleven molecules have speeds 15, 16, 17, … , 25 m/s. Calculate(a) vavg(b) vrms.
Suppose you place an ice cube in a beaker of room temperature water, then seal them in a rigid, well-insulated container. No energy can enter or leave the container.a. If you open the container an
The molecules in a six-particle gas have velocitiesCalculate(a) vavg,(b) vavg,(c) vrms. V1 = (20î – 30) m/s V2 = (40î + 70î) m/s V3 = (-80î + 20ĵ) m/s V = 30î m/s Vs = (40î – 407) m/s 36 =
The two containers of gas in FIGURE Q20.8 are in good thermal contact with each other but well insulated from the environment. They have been in contact for a long time and are in thermal
For a monatomic gas, what is the ratio of the volume per atom (V/N) to the volume of an atom when the mean free path is ten times the atomic diameter?

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