Understanding Energy Changes in an Ideal Gas Under Constant Temperature Conditions

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The energy change of an ideal gas during volume expansion at constant temperature is zero. When the gas expands against a vacuum, the opposing force is zero, leading to no change in internal energy (DU = 0). According to the first law of thermodynamics, the internal energy change can be expressed as the sum of temperature and volume derivatives. Since both the change in internal energy and temperature are zero, the relationship indicates that the partial derivative of internal energy with respect to volume at constant temperature is also zero, despite the volume change (DV ≠ 0).

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May 02, 2026

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Understanding Energy Changes in an Ideal Gas Under Constant Temperature Conditions

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The change of energy of an ideal gas with volume at constant temperature is equal to zero.AS GAS EXPANDS AGAINST VACCUM, THEREFORE ,POPPOSING=0HENCE DW=-POPPOSINGDV=0USINF FIRST LAW OF THERMODYNAMICSDU=đQ(∂u⁄∂v)t=0DU= (∂U⁄∂T)V+(∂U/∂V)TDVBUT DU=0 AND DT=0 HENCE (∂u⁄∂v)tDV=0AS DV≠0 IMPLIES THAT

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