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Condition |
free/or 0.5$ |
| 561 | A mercury drop shaped as a round tablet of radius R and thickness h is located between two horizontal glass plates. Assuming that h << R, find the mass m of a weight which has to be placed on the upper plate to diminish the distance between the plates n-times. The contact angle equals θ. Calculate m if R = 2.0 cm, h = 0.38 mm, n = 2.0, and θ = 135°. |
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| 562 | Find the attraction force between two parallel glass plates, separated by a distance h = 0.10 mm, after a water drop of mass m = 70 mg was introduced between them. The wetting is assumed to be complete. |
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| 563 | Two glass discs of radius R = 5.0 cm were wetted with water and put together so that the thickness of the water layer between them was h = 1.9 μm. Assuming the wetting to be complete, find the force that has to be applied at right angles to the plates in order to pull them apart. |
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| 564 | Two vertical parallel glass plates are partially submerged in water. The distance between the plates is d = 0.10 mm, and their width is L = 12 cm. Assuming that the water between the plates does not reach the upper edges of the plates and that the wetting is complete, find the force of their mutual attraction. |
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| 565 | Find the lifetime of a soap bubble of radius R connected with the atmosphere through a capillary of length L and inside radius r. The surface tension is a, the viscosity coefficient of the gas is n. |
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| 566 | A vertical capillary is brought in contact with the water surface. What amount of heat is liberated while the water rises along the capillary? The wetting is assumed to be complete, the surface tension equals α. |
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| 567 | Find the free energy of the surface layer of (a) a mercury droplet of diameter d = 1.4 mm; (b) a soap bubble of diameter d = 6.0 mm if the surface tension of the soap water solution is equal to a = 45 mN/m. |
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| 568 | Find the increment of the free energy of the surface layer when two identical mercury droplets, each of diameter d = 1.5 mm, merge isothermally. |
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| 569 | Find the work to be performed in order to blow a soap bubble of radius R if the outside air pressure is equal to p0, and the surface tension of the soap water solution is equal to a. |
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| 570 | A soap bubble of radius r is inflated with an ideal gas. The atmospheric pressure is po, the surface tension of the soap water solution is a. Find the difference between the molar heat capacity of the gas during its heating inside the bubble and the molar heat capacity of the gas under constant pressure, C — Cp. |
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| 571 | Considering the Carnot cycle as applied to a liquid film, show that in an isothermal process the amount of heat required for the formation of a unit area of the surface layer is equal to q = —T•da/dT, where daldT is the temperature derivative of the surface tension. |
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| 572 | The surface of a soap film was increased isothermally by ds at a temperature T. Knowing the surface tension of the soap water solution a and the temperature coefficient da/dT, find the increment (a) of the entropy of the film's surface layer; (b) of the internal energy of the surface layer. |
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| 573 | A saturated water vapour is contained in a cylindrical vessel under a weightless piston at a temperature t = 100 °C. As a result of a slow introduction of the piston a small fraction of the vapour Δm = 0.70 g gets condensed. What amount of work was performed over the gas? The vapour is assumed to be ideal, the volume of the liquid is to be neglected. |
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| 574 | A vessel of volume V = 6.0 l contains water together with its saturated vapour under a pressure of 40 atm and at a temperature of 250 °C. The specific volume of the vapour is equal to Vv' = 50 l/kg under these conditions. The total mass of the system water-vapour equals m = 5.0 kg. Find the mass and the volume of the vapour. |
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| 575 | The saturated water vapour is enclosed in a cylinder under a piston and occupies a volume V0 = 5.0 L at the temperature t = 100 °C. Find the mass of the liquid phase formed after the volume under the piston decreased isothermally to V = 1.6 L. The saturated vapour is assumed to be ideal. |
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| 576 | A volume occupied by a saturated vapour is reduced isothermally n-fold. Find what fraction ri of the final volume is occupied by the liquid phase if the specific volumes of the saturated vapour and the liquid phase differ by N times (N > n). Solve the same problem under the condition that the final volume of the substance corresponds to the midpoint of a horizontal portion of the isothermal line in the diagram p, V. |
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| 577 | An amount of water of mass m = 1.00 kg, boiling at standard atmospheric pressure, turns completely into saturated vapour. Assuming the saturated vapour to be an ideal gas find the increment of entropy and internal energy of the system. |
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| 578 | Water of mass m = 20 g is enclosed in a thermally insulated cylinder at the temperature of 0 °C under a weightless piston whose area is S = 410 cm2. The outside pressure is equal to standard atmospheric pressure. To what height will the piston rise when the water absorbs Q = 20.0 kJ of heat? |
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| 579 | One gram of saturated water vapour is enclosed in a thermally insulated cylinder under a weightless piston. The outside pressure being standard, m = 1.0 g of water is introduced into the cylinder at a temperature t0 = 22 °C. Neglecting the heat capacity of the cylinder and the friction of the piston against the cylinder's walls, find the work performed by the force of the atmospheric pressure during the lowering of the piston. |
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| 580 | If an additional pressure Δp of a saturated vapour over a convex spherical surface of a liquid is considerably less than the vapour pressure over a plane surface, then Δp = (ρv/ρl)2α/r, where ρv and ρl are the densities of the vapour and the liquid, α is the surface tension, and r is the radius of curvature of the surface. Using this formula, find the diameter of water droplets at which the saturated vapour pressure exceeds the vapour pressure over the plane surface by η = 1.0% at a temperature t = 27 °C. The vapour is assumed to be an ideal gas. |
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