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C | 10 |
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Question A quantity of a monatomic ideal gas expands to twice the volume while maintaining the same pressure. If the internal energy of the gas were U0 before the expansion, what is it after the expansion? | |
Answer 2 U0 | |
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| KillGorack | 2023-07-03 16:01:40 | The internal energy of an ideal monatomic gas is solely a function of its temperature. It does not depend on its volume or pressure. According to the Ideal Gas Law, PV = nRT, where: P is the pressure V is the volume n is the number of moles of the gas R is the ideal gas constant T is the temperature Given that the pressure is constant and the volume is doubled, the temperature of the gas must also double to maintain the equation. For a monatomic ideal gas, the internal energy U is proportional to the temperature T: U = (3/2)nRT Given that the temperature doubles, the internal energy U also doubles. Therefore, the internal energy after the expansion U_f is twice the initial internal energy U_0: U_f = 2U_0 This is a simplified model and assumes that the gas behaves ideally, that there are no intermolecular forces affecting the gas, and that all energy is in the form of kinetic energy (appropriate for a monatomic gas where there are no vibrational or rotational modes of energy). |