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free/or 0.5$ |
| 501 | In which case will the efficiency of a Carnot cycle be higher: when the hot body temperature is increased by ΔT, or when the cold body temperature is decreased by the same magnitude? |
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| 502 | Hydrogen is used in a Carnot cycle as a working substance. Find the efficiency of the cycle, if as a result of an adiabatic expansion (a) the gas volume increases n = 2.0 times; (b) the pressure decreases n = 2.0 times. |
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| 503 | A heat engine employing a Carnot cycle with an efficiency of η = 10% is used as a refrigerating machine, the thermal reservoirs being the same. Find its refrigerating efficiency ε. |
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| 504 | An ideal gas goes through a cycle consisting of alternate isothermal and adiabatic curves (Fig. 2.2). The isothermal processes proceed at the temperatures T1, T2, and T3. Find the efficiency of such a cycle, if in each isothermal expansion the gas volume increases in the same proportion. |
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| 505 | Find the efficiency of a cycle consisting of two isochoric and two adiabatic lines, if the volume of the ideal gas changes n = 10 times within the cycle. The working substance is nitrogen. |
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| 506 | Find the efficiency of a cycle consisting of two isobaric and two adiabatic lines, if the pressure changes n times within the cycle. The working substance is an ideal gas whose adiabatic exponent is equal to y. |
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| 507 | An ideal gas whose adiabatic exponent equals y goes through a cycle consisting of two isochoric and two isobaric lines. Find the efficiency of such a cycle, if the absolute temperature of the gas rises n times both in the isochoric heating and in the isobaric expansion. |
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| 508 | An ideal gas goes through a cycle consisting of (a) isochoric, adiabatic, and isothermal lines; (b) isobaric, adiabatic, and isothermal lines, with the isothermal process proceeding at the minimum temperature of the whole cycle. Find the efficiency of each cycle if the absolute temperature varies n-fold within the cycle. |
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| 509 | The conditions are the same as in the foregoing problem with the exception that the isothermal process proceeds at the maximum temperature of the whole cycle. |
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| 510 | An ideal gas goes through a cycle consisting of isothermal, polytropic, and adiabatic lines, with the isothermal process proceeding at the maximum temperature of the whole cycle. Find the efficiency of such a cycle if the absolute temperature varies n-fold within the cycle. |
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| 511 | An ideal gas with the adiabatic exponent y goes through a direct (clockwise) cycle consisting of adiabatic, isobaric, and isochoric lines. Find the efficiency of the cycle if in the adiabatic process the volume of the ideal gas (a) increases n-fold; (b) decreases n-fold. |
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| 512 | Calculate the efficiency of a cycle consisting of isothermal, isobaric, and isochoric lines, if in the isothermal process the volume of the ideal gas with the adiabatic exponent γ (a) increases n-fold; (b) decreases n-fold. |
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| 513 | Find the efficiency of a cycle consisting of two isochoric and two isothermal lines if the volume varies v-fold and the absolute temperature t-fold within the cycle. The working substance is an ideal gas with the adiabatic exponent y. |
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| 514 | Find the efficiency of a cycle consisting of two isobaric and two isothermal lines if the pressure varies n-fold and the absolute temperature y-fold within the cycle. The working substance is an ideal gas with the adiabatic exponent y. |
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| 515 | An ideal gas with the adiabatic exponent y goes through a cycle (Fig. 2.3) within which the absolute temperature varies t-fold. Find the efficiency of this cycle. |
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| 516 | Making use of the Clausius inequality, demonstrate that all cycles having the same maximum temperature Tmax and the same minimum temperature Tmin are less efficient compared to the Garnot cycle with the same Tmax and Tmin. |
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| 517 | Making use of the Carnot theorem, show that in the case of a physically uniform substance whose state is defined by the parameters T and V (aU/aV)T = T (dp/dT)v — p where U (T, V) is the internal energy of the substance. Instruction. Consider the infinitesimal Carnot cycle in the variables p, V. |
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| 518 | Find the entropy increment of one mole of carbon dioxide when its absolute temperature increases n = 2.0 times if the process of heating is (a) isochoric; (b) isobaric. The gas is to be regarded as ideal. |
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| 519 | The entropy of ν = 4.0 moles of an ideal gas increases by ΔS = 23 J/K due to the isothermal expansion. How many times should the volume ν = 4.0 moles of the gas be increased? |
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| 520 | Two moles of an ideal gas are cooled isochorically and then expanded isobarically to lower the gas temperature back to the initial value. Find the entropy increment of the gas if in this process the gas pressure changed n = 3.3 times. |
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