| № |
Condition |
free/or 0.5$ |
| 55723 | A house has well-insulated walls. It contains a volume of 100 m3 of air at 300 K.
(a) Calculate the energy required to increase the temperature of this diatomic ideal gas by 1.00°C.
(b) What If? If this energy could be used to lift an object of mass m through a height of 2.00 m, what is the value of m? |
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| 55724 | A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0°C. It is completely filled with turpentine and then slowly warmed to 80.0°C. (a) How much turpentine overflows? (b) If the cylinder is then cooled back to 20.0°C, how far below the cylinder’s rim does the turpentine’s surface recede? |
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| 55725 | Here is a clever idea. Suppose you build a two-engine device such that the exhaust energy output from one heat engine is the input energy for a second heat engine. We say that the two engines are running in series. Let e 1 and e 2 represent the efficiencies of the two engines.
(a) The overall efficiency of the two-engine device is defined as the total work output divided by the energy put into the first engine by heat. Show that the overall efficiency is given by |
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| 55726 | Help! One of our equations is missing! We describe constant acceleration motion with the variables and parameters vxi, vxf, ax, t, and xf - xi. Of the equations in Table 2.2, the first does not involve xf - xi . The second does not contain ax; the third omits vxf and the last leaves out t. So to complete the set there should be an equation not involving vxi. Derive it from the others. Use it to solve Problem 29 in one step. |
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| 55727 | Helium gas is sold in steel tanks. If the helium is used to inflate a balloon, could the balloon lift the spherical tank the helium came in? Justify your answer. Steel will rupture if subjected to tensile stress greater than its yield strength of 5 X 108 N/m2. Suggestion: You may consider a steel shell of radius r and thickness t containing helium at high pressure and on the verge of breaking apart into two hemispheres. |
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| 55728 | Helium gas is in thermal equilibrium with liquid helium at 4.20 K. Even though it is on the point of condensation, model the gas as ideal and determine the most probable speed of a helium atom (mass = 6.64 X 10-27 kg) in it. |
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| 55729 | A heat pump, shown in Figure P22.26, is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose that the ratio of the actual energy entering the room to the work done by the device’s motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor, given that the inside temperature is 20.0°C and the outside temperature is "5.00°C |
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| 55730 | A heat pump is to be installed in a region where the average outdoor temperature in the winter months is - 20°C. In view of this, why would it be advisable to place the outdoor compressor unit deep in the ground? Why are heat pumps not commonly used for heating in cold climates? |
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| 55731 | Heat engine X takes in four times more energy by heat from the hot reservoir than heat engine Y. Engine X delivers two times more work, and it rejects seven times more energy by heat to the cold reservoir than heat engine Y. Find the efficiency of
(a) Heat engine X and
(b) Heat engine Y. |
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| 55732 | A heat engine takes in 360 J of energy from a hot reservoir and performs 25.0 J of work in each cycle. Find
(a) The efficiency of the engine and
(b) The energy expelled to the cold reservoir in each cycle. |
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| 55733 | A heat engine performs 200 J of work in each cycle and has an efficiency of 30.0%. For each cycle, how much energy is:
(a) Taken in and
(b) Expelled by heat? |
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| 55734 | A heat engine operating between 200°C and 80.0°C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work? |
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| 55735 | A heat engine operates between two reservoirs at T2 = 600 K and T1 = 350 K. It takes in 1 000 J of energy from the higher-temperature reservoir and performs 250 J of work. Find
(a) The entropy change of the Universe ΔSU for this process and
(b) The work W that could have been done by an ideal Carnot engine operating between these two reservoirs.
(c) Show that the difference between the amounts of work done in parts (a) and (b) is T1ΔSU. |
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| 55736 | A hare and a tortoise compete in a race over a course 1.00 km long. The tortoise crawls straight and steadily at its maximum speed of 0.200 m/s toward the finish line. The hare runs at its maximum speed of 8.00 m/s toward the goal for 0.800 km and then stops to tease the tortoise. How close to the goal can the hare let the tortoise approach before resuming the race, which the tortoise wins in a photo finish? Assume that, when moving, both animals move steadily at their respective maximum speeds. |
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| 55737 | A hard rubber ball, released at chest height, falls to the pavement and bounces back to nearly the same height. When it is in contact with the pavement, the lower side of the ball is temporarily flattened. Suppose that the maximum depth of the dent is on the order of 1 cm. Compute an order-of-magnitude estimate for the maximum acceleration of the ball while it is in contact with the pavement. State your assumptions, the quantities you estimate, and the values you estimate for them. |
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| 55738 | A hammer head H having a weight of 0.25 lb is moving vertically downward at 40 ft/s when it strikes the head of a nail of negligible mass and drives it into a block of wood. Find the impulse on the nail if it is assumed that the grip at A is loose, the handle has a negligible mass, and the hammer stays in contact with the nail while It comes to rest. Neglect the impulse caused by the weight of the hammer head during contact with the nail. |
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| 55739 | A golf ball is released from rest from the top of a very tall building. Neglecting air resistance, calculate
(a) The position and
(b) The velocity of the ball after 1.00, 2.00, and 3.00 s |
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| 55740 | A glider on an air track carries a flag of length l through a stationary photo gate, which measures the time interval ∆td during which the flag blocks a beam of infrared light passing across the photo gate. The ratio vd l / ∆td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration.
(a) Argue for or against the idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photo gate in space.
(b) Argue for or against the idea that vd is equal to the instantaneous velocity of the glider when it is halfway through the photo gate in time. |
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| 55741 | A glass window pane has an area of 3.00 m2 and a thickness of 0.600 cm. If the temperature difference between its faces is 25.0°C, what is the rate of energy transfer by conduction through the window? |
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| 55742 | Given that the rms speed of a helium atom at a certain temperature is 1 350 m/s, find by proportion the rms speed of an oxygen (O2) molecule at this temperature. The molar mass of O2 is 32.0 g/mol, and the molar mass of He is 4.00 g/mol. |
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