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421Calculate the value of γ = Cp/CV for a gaseous mixture consisting of ν1 = 2.0 moles of oxygen and ν2 = 3.0 moles of carbon dioxide. The gases are assumed to be ideal.
calculate-the-value-of-cp-cv-for-a-gaseous-mixture-cons
422Find the specific heat capacities cv and cp for a gaseous mixture consisting of 7.0 g of nitrogen and 20 g of argon. The gases are assumed to be ideal.
find-the-specific-heat-capacities-cv-and-cp-for-a-gaseous-mi
423One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere. What work has to be performed in order to increase isothermally the gas volume under the piston n times by slowly raising the piston? The friction of the piston against the cylinder walls is negligibly small.
one-mole-of-a-certain-ideal-gas-is-contained-under-a-weightl
424A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume V0, in which an ideal gas is contained under the same pressure p0 and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas η times compared to that of the other by slowly moving the piston?
a-piston-can-freely-move-inside-a-horizontal-cylinder-closed
425Three moles of an ideal gas being initially at a temperature T0 = 273 K were isothermally expanded n = 5.0 times its initial volume and then isochorically heated so that the pressure in the final state became equal to that in the initial state. The total amount of heat transferred to the gas during the process equals Q = 80 kJ. Find the ratio γ = Cp/CV for this gas.
three-moles-of-an-ideal-gas-being-initially-at-a-temperature
426Draw the approximate plots of isochoric, isobaric, isothermal, and adiabatic processes for the case of an ideal gas, using the following variables: (a) p, T; (b) V, T.
draw-the-approximate-plots-of-isochoric-isobaric-isotherma
427One mole of oxygen being initially at a temperature T0 = 290 K is adiabatically compressed to increase its pressure η = 10.0 times. Find: (a) the gas temperature after the compression; (b) the work that has been performed on the gas.
one-mole-of-oxygen-being-initially-at-a-temperature-t0-290
428A certain mass of nitrogen was compressed η = 5.0 times (in terms of volume), first adiabatically, and then isothermally. In both cases the initial state of the gas was the same. Find the ratio of the respective works expended in each compression.
a-certain-mass-of-nitrogen-was-compressed-5-0-times-in
429A heat-conducting piston can freely move inside a closed thermally insulated cylinder with an ideal gas. In equilibrium the piston divides the cylinder into two equal parts, the gas temperature being equal to T0. The piston is slowly displaced. Find the gas temperature as a function of the ratio η of the volumes of the greater and smaller sections. The adiabatic exponent of the gas is equal to γ.
a-heat-conducting-piston-can-freely-move-inside-a-closed-the
430Find the rate v with which helium flows out of a thermally insulated vessel into vacuum through a small hole. The flow rate of the gas inside the vessel is assumed to be negligible under these conditions. The temperature of helium in the vessel is T = 1,000 K.
find-the-rate-v-with-which-helium-flows-out-of-a-thermally-i
431The volume of one mole of an ideal gas with the adiabatic exponent γ is varied according to the law V = a/T, where a is a constant. Find the amount of heat obtained by the gas in this process if the gas temperature increased by ΔT.
the-volume-of-one-mole-of-an-ideal-gas-with-the-adiabatic-ex
432Demonstrate that the process in which the work performed by an ideal gas is proportional to the corresponding increment of its internal energy is described by the equation pVn = const, where n is a constant.
demonstrate-that-the-process-in-which-the-work-performed-by
433Find the molar heat capacity of an ideal gas in a polytropic process pVn = const if the adiabatic exponent of the gas is equal to γ. At what values of the polytropic constant n will the heat capacity of the gas be negative?
find-the-molar-heat-capacity-of-an-ideal-gas-in-a-polytropic
434In a certain polytropic process the volume of argon was increased α = 4.0 times. Simultaneously, the pressure decreased β = 8.0 times. Find the molar heat capacity of argon in this process, assuming the gas to be ideal.
in-a-certain-polytropic-process-the-volume-of-argon-was-incr
435One mole of argon is expanded polytropically, the polytropic constant being n = 1.50. In the process, the gas temperature changes by ΔT = -26 K. Find: (a) the amount of heat obtained by the gas; (b) the work performed by the gas.
one-mole-of-argon-is-expanded-polytropically-the-polytropic
436An ideal gas whose adiabatic exponent equals γ is expanded according to the law p = αV, where α is constant. The initial volume of the gas is equal to V0. As a result of expansion the volume increases η times. Find: (a) the increment of the internal energy of the gas; (b) the work performed by the gas; (c) the molar heat capacity of the gas in the process.
an-ideal-gas-whose-adiabatic-exponent-equals-is-expanded
437An ideal gas whose adiabatic exponent equals γ is expanded so that the amount of heat transferred to the gas is equal to the decrease of its internal energy. Find: (a) the molar heat capacity of the gas in this process; (b) the equation of the process in the variables T, V; (c) the work performed by one mole of the gas when its volume increases η times if the initial temperature of the gas is T0.
an-ideal-gas-whose-adiabatic-exponent-equals-is-expanded
438One mole of an ideal gas whose adiabatic exponent equals y undergoes a process in which the gas pressure relates to the temperature as p = aT^alfa, where a and alfa are constants. Find: (a) the work performed by the gas if its temperature gets an increment AT; (b) the molar heat capacity of the gas in this process; at what value of a will the heat capacity be negative?
one-mole-of-an-ideal-gas-whose-adiabatic-exponent-equals-y-u
439An ideal gas with the adiabatic exponent γ undergoes a process in which its internal energy relates to the volume as U = aVα, where a and α are constants. Find: (a) the work performed by the gas and the amount of heat to be transferred to this gas to increase its internal energy by ΔU; (b) the molar heat capacity of the gas in this process.
an-ideal-gas-with-the-adiabatic-exponent-undergoes-a-proc
440An ideal gas has a molar heat capacity Cv at constant volume. Find the molar heat capacity of this gas as a function of its volume V, if the gas undergoes the following process: (a) T = T0e^(αV); (b) p = p0e^(αV), where T0, p0 and α are constants.
an-ideal-gas-has-a-molar-heat-capacity-cv-at-constant-volume
 
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