№ |
Condition |
free/or 0.5$ |
441 | One mole of an ideal gas whose adiabatic exponent equals γ undergoes a process p = p0 + α/V, where p0 and α are positive constants. Find: (a) heat capacity of the gas as a function of its volume; (b) the internal energy increment of the gas, the work performed by it, and the amount of heat transferred to the gas, if its volume increased from V1 to V2. |
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442 | One mole of an ideal gas with heat capacity at constant pressure Cp undergoes the process T = T0 + αV, where T0 and α are constants. Find: (a) heat capacity of the gas as a function of its volume; (b) the amount of heat transferred to the gas, if its volume increased from V1 to V2. |
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443 | For the case of an ideal gas find the equation of the process (in the variables T, V) in which the molar heat capacity varies as: (a) C = CV + αT; (b) C = CV + βV; (c) C = CV + ap, where α, β and a are constants. |
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444 | An ideal gas has an adiabatic exponent γ. In some process its molar heat capacity varies as C = α/T, where α is a constant. Find: (a) the work performed by one mole of the gas during its heating from the temperature T0 to the temperature η times higher; (b) the equation of the process in the variables p, V. |
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445 | Find the work performed by one mole of a Van der Waals gas during its isothermal expansion from the volume V1 to V2 at a temperature T. |
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446 | One mole of oxygen is expanded from a volume V1 = 1.00 L to V2 = 5.0 L at a constant temperature T = 280 K. Calculate: (a) the increment of the internal energy of the gas: (b) the amount of the absorbed heat. The gas is assumed to be a Van der Waals gas. |
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447 | For a Van der Waals gas find: (a) the equation of the adiabatic curve in the variables T, V; (b) the difference of the molar heat capacities Cp — Cv as a function of T and V. |
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448 | Two thermally insulated vessels are interconnected by a tube equipped with a valve. One vessel of volume V1 = 10 l contains ν = 2.5 moles of carbon dioxide. The other vessel of volume V2 = 100 l is evacuated. The valve having been opened, the gas adiabatically expanded. Assuming the gas to obey the Van der Waals equation, find its temperature change accompanying the expansion. |
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449 | What amount of heat has to be transferred to v = 3.0 moles of carbon dioxide to keep its temperature constant while it expands into vacuum from the volume V1 = 5.0 L to V2 =10 L? The gas is assumed to be a Van der Waals gas. |
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450 | Modern vacuum pumps permit the pressures down to p = 4*10-15 atm to be reached at room temperatures. Assuming that the gas exhausted is nitrogen, find the number of its molecules per 1 cm3 and the mean distance between them at this pressure. |
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451 | A vessel of volume V = 5.0 l contains m = 1.4 g of nitrogen at a temperature T = 1800 K. Find the gas pressure, taking into account that η = 30% of molecules are disassociated into atoms at this temperature. |
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452 | Under standard conditions the density of the helium and nitrogen mixture equals ρ = 0.60 g/l. Find the concentration of helium atoms in the given mixture. |
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453 | A parallel beam of nitrogen molecules moving with velocity v = 400 m/s impinges on a wall at an angle θ = 30° to its normal. The concentration of molecules in the beam n = 0.9*1019 cm-3. Find the pressure exerted by the beam on the wall assuming the molecules to scatter in accordance with the perfectly elastic collision law. |
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454 | How many degrees of freedom have the gas molecules, if under standard conditions the gas density is ρ = 1.3 mg/cm3 and the velocity of sound propagation in it is v = 330 m/s. |
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455 | Determine the ratio of the sonic velocity v in a gas to the root mean square velocity of molecules of this gas, if the molecules are (a) monatomic; (b) rigid diatomic. |
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456 | A gas consisting of N-atomic molecules has the temperature T at which all degrees of freedom (translational, rotational, and vibrational) are excited. Find the mean energy of molecules in such a gas. What fraction of this energy corresponds to that of translational motion? |
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457 | Suppose a gas is heated up to a temperature at which all degrees of freedom (translational, rotational, and vibrational) of its molecules are excited. Find the molar heat capacity of such a gas in the isochoric process, as well as the adiabatic exponent γ, if the gas consists of (a) diatomic; (b) linear N-atomic; (c) network N-atomic molecules. |
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458 | An ideal gas consisting of N-atomic molecules is expanded isobarically. Assuming that all degrees of freedom (translational, rotational, and vibrational) of the molecules are excited, find what fraction of heat transferred to the gas in this process is spent to perform the work of expansion. How high is this fraction in the case of a monatomic gas? |
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459 | Find the molar mass and the number of degrees of freedom of molecules in a gas if its heat capacities are known: cv = 0.65 J/(g*K) and cp = 0.91 J/(g*K). |
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460 | Find the number of degrees of freedom of molecules in a gas whose molar heat capacity (a) at constant pressure is equal to Cp = 29 J/(mol.K); (b) is equal to C = 29 J/(mol·K) in the process pT = const. |
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