An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n . The internal energy of one mole of the gas is U n and the speed of sound in the gas is v n . At a fixed temperature and pressure, which of the following is the correct option?
C. v 5 > v 7 and U 5 < U 7
As we know, internal energy of one mole of the gas U n = n R T 2 . Clearly, U n ∝ n , where n is degree of freedom. Therefore, as n increases, U n also increases. Now, speed of sound in gas v n = γ R T M = 1 + 2 n R T M Clearly, as n increases and v n decreases. Hence, U 7 > U 5 and U 7 > U 6 and v 5 > v 7 .
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