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Condition |
free/or 0.5$ |
| 521 | Helium of mass m = 1.7 g is expanded adiabatically n = 3.0 times and then compressed isobarically down to the initial volume. Find the entropy increment of the gas in this process. |
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| 522 | Find the entropy increment of ν = 2.0 moles of an ideal gas whose adiabatic exponent γ = 1.30 if, as a result of a certain process, the gas volume increased α = 2.0 times while the pressure dropped β = 3.0 times. |
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| 523 | Vessels 1 and 2 contain ν = 1.2 moles of gaseous helium. The ratio of the vessels' volumes V2/V1 = α = 2.0, and the ratio of the absolute temperatures of helium in them T1/T2 = β = 1.5. Assuming the gas to be ideal, find the difference of gas entropies in these vessels, S2 - S1. |
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| 524 | One mole of an ideal gas with the adiabatic exponent γ goes through a polytropic process as a result of which the absolute temperature of the gas increases τ-fold. The polytropic constant equals n. Find the entropy increment of the gas in this process. |
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| 525 | The expansion process of ν = 2.0 moles of argon proceeds so that the gas pressure increases in direct proportion to its volume. Find the entropy increment of the gas in this process provided its volume increases α = 2.0 times. |
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| 526 | An ideal gas with the adiabatic exponent γ goes through a process p = p0 - αV, where p0 and α are positive constants, and V is the volume. At what volume will the gas entropy have the maximum value? |
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| 527 | One mole of an ideal gas goes through a process in which the entropy of the gas changes with temperature T as S = aT + Cv ln T, where a is a positive constant, Cv is the molar heat capacity of this gas at constant volume. Find the volume dependence of the gas temperature in this process if T = T0 at V = V0. |
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| 528 | Find the entropy increment of one mole of a Van der Waals gas due to the isothermal variation of volume from V1 to V2. The Van der Waals corrections are assumed to be known. |
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| 529 | One mole of a Van der Waals gas which had initially the volume V1 and the temperature T1 was transferred to the state with the volume V2 and the temperature T2. Find the corresponding entropy increment of the gas, assuming its molar heat capacity Cv to be known. |
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| 530 | At very low temperatures the heat capacity of crystals is equal to C = aT3^, where a is a constant. Find the entropy of a crystal as a function of temperature in this temperature interval. |
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| 531 | Find the entropy increment of an aluminum bar of mass m = 3.0 kg on its heating from the temperature T1 = 300 K up to T2 = 600 K if in this temperature interval the specific heat capacity of aluminum varies as c = a + bT, where a = 0.77 J/(g*K), b = 0.46 mJ/(g*K2). |
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| 532 | In some process the temperature of a substance depends on its entropy S as T = aSn, where a and n are constants. Find the corresponding heat capacity C of the substance as a function of S. At what condition is C < 0? |
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| 533 | Find the temperature T as a function of the entropy S of a substance for a polytropic process in which the heat capacity of the substance equals C. The entropy of the substance is known to be equal to S0 at the temperature T0. Draw the approximate plots T(S) for C > 0 and C < 0. |
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| 534 | One mole of an ideal gas with heat capacity Cv goes through a process in which its entropy S depends on T as S = α/T, where α is a constant. The gas temperature varies from T1 to T2. Find: (a) the molar heat capacity of the gas as a function of its temperature; (b) the amount of heat transferred to the gas; (c) the work performed by the gas. |
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| 535 | A working substance goes through a cycle within which the absolute temperature varies n-fold, and the shape of the cycle is shown in (a) Fig. 2.4a; (b) Fig. 2.4b, where T is the absolute temperature, and S the entropy. Find the efficiency of each cycle. |
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| 536 | One of the two thermally insulated vessels interconnected by a tube with a valve contains ν = 2.2 moles of an ideal gas. The other vessel is evacuated. The valve having been opened, the gas increased its volume n = 3.0 times. Find the entropy increment of the gas. |
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| 537 | A weightless piston divides a thermally insulated cylinder into two equal parts. One part contains one mole of an ideal gas with adiabatic exponent γ, the other is evacuated. The initial gas temperature is T0. The piston is released and the gas fills the whole volume of the cylinder. Then the piston is slowly displaced back to the initial position. Find the increment of the internal energy and the entropy of the gas resulting from these two processes. |
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| 538 | An ideal gas was expanded from the initial state to the volume V without any heat exchange with the surrounding bodies. Will the final gas pressure be the same in the case of (a) a fast and in the case of (b) a very slow expansion process? |
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| 539 | A thermally insulated vessel is partitioned into two parts so that the volume of one part is n = 2.0 times greater than that of the other. The smaller part contains v1 = 0.30 mole of nitrogen, and the greater one v2 = 0.70 mole of oxygen. The temperature of the gases is the same. A hole is punctured in the partition and the gases are mixed. Find the corresponding increment of the system's entropy, assuming the gases to be ideal. |
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| 540 | A piece of copper of mass m1 = 300 g with initial temperature t1 = 97 °C is placed into a calorimeter in which the water of mass m2 = 100 g is at a temperature t2 = 7 °C. Find the entropy increment of the system by the moment the temperatures equalize. The heat capacity of the calorimeter itself is negligibly small. |
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