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Condition |
free/or 0.5$ |
| 461 | Find the adiabatic exponent γ for a mixture consisting of ν1 moles of a monatomic gas and ν2 moles of gas of rigid diatomic molecules. |
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| 462 | A thermally insulated vessel with gaseous nitrogen at a temperature t = 27 °C moves with velocity v = 100 m/s. How much (in per cent) and in what way will the gas pressure change on a sudden stoppage of the vessel? |
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| 463 | Calculate at the temperature t = 17 °C: (a) the root mean square velocity and the mean kinetic energy of an oxygen molecule in the process of translational motion; (b) the root mean square velocity of a water droplet of diameter d = 0.10 μm suspended in the air. |
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| 464 | A gas consisting of rigid diatomic molecules is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of the molecules η = 1.50 times? |
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| 465 | The mass m = 15 g of nitrogen is enclosed in a vessel at a temperature T = 300 K. What amount of heat has to be transferred to the gas to increase the root mean square velocity of its molecules η = 2.0 times? |
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| 466 | The temperature of a gas consisting of rigid diatomic molecules is T = 300 K. Calculate the angular root mean square velocity of a rotating molecule if its moment of inertia is equal to I = 2.1·10^(-39) g·cm2. |
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| 467 | A gas consisting of rigid diatomic molecules was initially under standard conditions. Then the gas was compressed adiabatically η = 5.0 times. Find the mean kinetic energy of a rotating molecule in the final state. |
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| 468 | How will the rate of collisions of rigid diatomic molecules against the vessel's wall change, if the gas is expanded adiabatically η times? |
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| 469 | The volume of gas consisting of rigid diatomic molecules was increased η = 2.0 times in a polytropic process with the molar heat capacity C = R. How many times will the rate of collisions of molecules against a vessel's wall be reduced as a result of this process? |
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| 470 | A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process. |
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| 471 | Calculate the most probable, the mean, and the root mean square velocities of a molecule of a gas whose density under standard atmospheric pressure is equal to r |
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| 472 | Find the fraction of gas molecules whose velocities differ by less than dn = 1.00% from the value of (a) the most probable velocity; (b) the root mean square velocity. |
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| 473 | Determine the gas temperature at which (a) the root mean square velocity of hydrogen molecules exceeds their most probable velocity by Δv = 400 m/s; (b) the velocity distribution function F(v) for the oxygen molecules will have the maximum value at the velocity v = 420 m/s. |
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| 474 | In the case of gaseous nitrogen find: (a) the temperature at which the velocities of the molecules v1 = 300 m/s and v2 = 600 m/s are associated with equal values of the Maxwell distribution function F(v); (b) the velocity of the molecules v at which the value of the Maxwell distribution function F(v) for the temperature T0 will be the same as that for the temperature η times higher. |
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| 475 | At what temperature of a nitrogen and oxygen mixture do the most probable velocities of nitrogen and oxygen molecules differ by dn = 30 m/s? |
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| 476 | The temperature of a hydrogen and helium mixture is T 300 K. At what value of the molecular velocity v will the Maxwell distribution function F (v) yield the same magnitude for both gases? |
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| 477 | At what temperature of a gas will the number of molecules, whose velocities fall within the given interval from v to v + dv, be the greatest? The mass of each molecule is equal to m. |
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| 478 | Find the fraction of molecules whose velocity projections on the x axis fall within the interval from vx to vx+dvx, while the moduli of perpendicular velocity components fall within the interval from v_|_ t o v_|_ + dv_|_. The mass of each molecule is m, and the temperature is T. |
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| 479 | Using the Maxwell distribution function, calculate the mean velocity projection <vx> and the mean value of the modulus of this projection <|vx|> if the mass of each molecule is equal to m and the gas temperature is T.. |
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| 480 | From the Maxwell distribution function find <vx2>, the mean value of the squared vx projection of the molecular velocity in a gas at a temperature T. The mass of each molecule is equal to m. |
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