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Condition |
free/or 0.5$ |
| 541 | Two identical thermally insulated vessels interconnected by a tube with a valve contain one mole of the same ideal gas each. The gas temperature in one vessel is equal to T1 a nd in the other, T2. The molar heat capacity of the gas of constant volume equals Cv. The valve having been opened, the gas comes to a new equilibrium state. Find the entropy increment dS of the gas. Demonstrate that dS > 0. |
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| 542 | N atoms of gaseous helium are enclosed in a cubic vessel of volume 1.0 cm3 at room temperature. Find: (a) the probability of atoms gathering in one half of the vessel; (b) the approximate numerical value of N ensuring the occurrence of this event within the time interval t ≈ 1010 years (the age of the Universe). |
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| 543 | Find the statistical weight of the most probable distribution of N = 10 identical molecules over two halves of the cylinder's volume. Find also the probability of such a distribution. |
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| 544 | A vessel contains N molecules of an ideal gas. Dividing mentally the vessel into two halves A and B, find the probability that the half A contains n molecules. Consider the cases when N = 5 and n = 0, 1, 2, 3, 4, 5. |
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| 545 | A vessel of volume V0 contains N molecules of an ideal gas. Find the probability of n molecules getting into a certain separated part of the vessel of volume V. Examine, in particular, the case V = V0/2. |
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| 546 | An ideal gas is under standard conditions. Find the diameter of the sphere within whose volume the relative fluctuation of the number of molecules is equal to i = 1.0·10^(-3). What is the average number of molecules inside such a sphere? |
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| 547 | One mole of an ideal gas consisting of monatomic molecules is enclosed in a vessel at a temperature T0 = 300 K. How many times and in what way will the statistical weight of this system (gas) vary if it is heated isochorically by dT = 1.0 K? |
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| 548 | Find the capillary pressure (a) in mercury droplets of diameter d = 1.5 pm; (b) inside a soap bubble of diameter d = 3.0 mm if the surface tension of the soap water solution is a = 45 mN/m. |
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| 549 | In the bottom of a vessel with mercury there is a round hole of diameter d = 70 μm. At what maximum thickness of the mercury layer will the liquid still not flow out through this hole? |
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| 550 | A vessel filled with air under pressure P0 contains a soap bubble of diameter d. The air pressure having been reduced isothermally n-fold, the bubble diameter increased n-fold. Find the surface tension of the soap water solution. |
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| 551 | Find the pressure in an air bubble of diameter d = 4.0 pm, located in water at a depth h = 5.0 m. The atmospheric pressure has the standard value P0. |
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| 552 | The diameter of a gas bubble formed at the bottom of a pond is d = 4.0 nm. When the bubble rises to the surface its diameter increases n = 1.1 times. Find how deep is the pond at that spot. The atmospheric pressure is standard, the gas expansion is assumed to be isothermal. |
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| 553 | Find the difference in height of mercury columns in two communicating vertical capillaries whose diameters are d1 = 0.50 mm and d2 = 1.00 mm, if the contact angle θ = 138°. |
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| 554 | A vertical capillary with inside diameter 0.50 mm is submerged into water so that the length of its part protruding over the water surface is equal to h = 25 mm. Find the curvature radius of the meniscus. |
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| 555 | A glass capillary of length L = 110 mm and inside diameter d = 20 nm is submerged vertically into water. The upper end of the capillary is sealed. The outside pressure is standard. To what length x has the capillary to be submorged to make the water levels inside and outside the capillary coincide? |
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| 556 | When a vertical capillary of length 1 with the sealed upper end was brought in contact with the surface of a liquid, the level of this liquid rose to the height h. The liquid density is p, the inside diameter of the capillary is d, the contact angle is f, the atmospheric pressure is P0. Find the surface tension of the liquid. |
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| 557 | A glass rod of diameter d1 = 1.5 mm is inserted symmetrically into a glass capillary with inside diameter d2 = 2.0 mm. Then the whole arrangement is vertically oriented and brought in contact with the surface of water. To what height will the water rise in the capillary? |
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| 558 | Two vertical plates submerged partially in a wetting liquid form a wedge with a very small angle 6cp. The edge of this wedge is vertical. The density of the liquid is p, its surface tension is a, the contact angle is f. Find the height h, to which the liquid rises, as a function of the distance x from the edge. |
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| 559 | A vertical water jet flows out of a round hole. One of the horizontal sections of the jet has the diameter d = 2.0 mm while the other section located l = 20 mm lower has the diameter which is n = 1.5 times less. Find the volume of the water flowing from the hole each second. |
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| 560 | A water drop falls in air with a uniform velocity. Find the difference between the curvature radii of the drop's surface at the upper and lower points of the drop separated by the distance h = 2.3 mm. |
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